id	sid	tid	token	lemma	pos
ejpam-5611	1	1	european	european	PROPN
ejpam-5611	1	2	journal	journal	PROPN
ejpam-5611	1	3	of	of	ADP
ejpam-5611	1	4	pure	pure	ADJ
ejpam-5611	1	5	and	and	CCONJ
ejpam-5611	1	6	applied	applied	ADJ
ejpam-5611	1	7	mathematics	mathematic	NOUN
ejpam-5611	1	8	2025	2025	NUM
ejpam-5611	1	9	,	,	PUNCT
ejpam-5611	1	10	vol	vol	NOUN
ejpam-5611	1	11	.	.	PROPN
ejpam-5611	1	12	18	18	NUM
ejpam-5611	1	13	,	,	PUNCT
ejpam-5611	1	14	issue	issue	NOUN
ejpam-5611	1	15	2	2	NUM
ejpam-5611	1	16	,	,	PUNCT
ejpam-5611	1	17	article	article	NOUN
ejpam-5611	1	18	number	number	NOUN
ejpam-5611	1	19	5611	5611	NUM
ejpam-5611	1	20	issn	issn	PROPN
ejpam-5611	1	21	1307	1307	NUM
ejpam-5611	1	22	-	-	SYM
ejpam-5611	1	23	5543	5543	NUM
ejpam-5611	1	24	–	–	PUNCT
ejpam-5611	1	25	ejpam.com	ejpam.com	X
ejpam-5611	1	26	published	publish	VERB
ejpam-5611	1	27	by	by	ADP
ejpam-5611	1	28	new	new	PROPN
ejpam-5611	1	29	york	york	PROPN
ejpam-5611	1	30	business	business	PROPN
ejpam-5611	1	31	global	global	PROPN
ejpam-5611	1	32	the	the	DET
ejpam-5611	1	33	saks	sak	NOUN
ejpam-5611	1	34	-	-	PUNCT
ejpam-5611	1	35	henstock	henstock	NOUN
ejpam-5611	1	36	lemma	lemma	PROPN
ejpam-5611	1	37	and	and	CCONJ
ejpam-5611	1	38	the	the	DET
ejpam-5611	1	39	change	change	NOUN
ejpam-5611	1	40	of	of	ADP
ejpam-5611	1	41	variable	variable	ADJ
ejpam-5611	1	42	formula	formula	NOUN
ejpam-5611	1	43	of	of	ADP
ejpam-5611	1	44	the	the	DET
ejpam-5611	1	45	pu	pu	PROPN
ejpam-5611	1	46	integral	integral	PROPN
ejpam-5611	1	47	greig	greig	PROPN
ejpam-5611	1	48	bates	bates	PROPN
ejpam-5611	1	49	c.	c.	PROPN
ejpam-5611	1	50	flores1,∗	flores1,∗	PROPN
ejpam-5611	1	51	,	,	PUNCT
ejpam-5611	1	52	ann	ann	PROPN
ejpam-5611	1	53	leslie	leslie	PROPN
ejpam-5611	1	54	v.	v.	CCONJ
ejpam-5611	1	55	flores1	flores1	PROPN
ejpam-5611	1	56	1	1	NUM
ejpam-5611	1	57	department	department	NOUN
ejpam-5611	1	58	of	of	ADP
ejpam-5611	1	59	mathematics	mathematic	NOUN
ejpam-5611	1	60	,	,	PUNCT
ejpam-5611	1	61	central	central	ADJ
ejpam-5611	1	62	mindanao	mindanao	PROPN
ejpam-5611	1	63	university	university	NOUN
ejpam-5611	1	64	,	,	PUNCT
ejpam-5611	1	65	maramag	maramag	NOUN
ejpam-5611	1	66	,	,	PUNCT
ejpam-5611	1	67	bukidnon	bukidnon	NOUN
ejpam-5611	1	68	,	,	PUNCT
ejpam-5611	1	69	philippines	philippine	NOUN
ejpam-5611	1	70	abstract	abstract	ADJ
ejpam-5611	1	71	.	.	PUNCT
ejpam-5611	2	1	henstock	henstock	PROPN
ejpam-5611	2	2	integral	integral	ADJ
ejpam-5611	2	3	is	be	AUX
ejpam-5611	2	4	a	a	DET
ejpam-5611	2	5	generalized	generalized	ADJ
ejpam-5611	2	6	version	version	NOUN
ejpam-5611	2	7	of	of	ADP
ejpam-5611	2	8	the	the	DET
ejpam-5611	2	9	riemann	riemann	PROPN
ejpam-5611	2	10	integral	integral	ADJ
ejpam-5611	2	11	and	and	CCONJ
ejpam-5611	2	12	in	in	ADP
ejpam-5611	2	13	most	most	ADJ
ejpam-5611	2	14	cases	case	NOUN
ejpam-5611	2	15	,	,	PUNCT
ejpam-5611	2	16	it	it	PRON
ejpam-5611	2	17	is	be	AUX
ejpam-5611	2	18	more	more	ADV
ejpam-5611	2	19	general	general	ADJ
ejpam-5611	2	20	than	than	ADP
ejpam-5611	2	21	the	the	DET
ejpam-5611	2	22	lebesgue	lebesgue	NOUN
ejpam-5611	2	23	integral	integral	ADJ
ejpam-5611	2	24	that	that	PRON
ejpam-5611	2	25	is	be	AUX
ejpam-5611	2	26	not	not	PART
ejpam-5611	2	27	constructed	construct	VERB
ejpam-5611	2	28	through	through	ADP
ejpam-5611	2	29	a	a	DET
ejpam-5611	2	30	measure	measure	NOUN
ejpam-5611	2	31	theoretic	theoretic	ADJ
ejpam-5611	2	32	standpoint	standpoint	NOUN
ejpam-5611	2	33	.	.	PUNCT
ejpam-5611	3	1	the	the	DET
ejpam-5611	3	2	pu	pu	PROPN
ejpam-5611	3	3	integral	integral	ADJ
ejpam-5611	3	4	,	,	PUNCT
ejpam-5611	3	5	on	on	ADP
ejpam-5611	3	6	one	one	NUM
ejpam-5611	3	7	hand	hand	NOUN
ejpam-5611	3	8	,	,	PUNCT
ejpam-5611	3	9	is	be	AUX
ejpam-5611	3	10	a	a	DET
ejpam-5611	3	11	henstock	henstock	NOUN
ejpam-5611	3	12	type	type	NOUN
ejpam-5611	3	13	that	that	PRON
ejpam-5611	3	14	utilizes	utilize	VERB
ejpam-5611	3	15	the	the	DET
ejpam-5611	3	16	notion	notion	NOUN
ejpam-5611	3	17	of	of	ADP
ejpam-5611	3	18	a	a	DET
ejpam-5611	3	19	partition	partition	NOUN
ejpam-5611	3	20	of	of	ADP
ejpam-5611	3	21	unity	unity	NOUN
ejpam-5611	3	22	.	.	PUNCT
ejpam-5611	4	1	in	in	ADP
ejpam-5611	4	2	this	this	DET
ejpam-5611	4	3	paper	paper	NOUN
ejpam-5611	4	4	,	,	PUNCT
ejpam-5611	4	5	the	the	DET
ejpam-5611	4	6	saks	sak	NOUN
ejpam-5611	4	7	-	-	PUNCT
ejpam-5611	4	8	henstock	henstock	NOUN
ejpam-5611	4	9	lemma	lemma	PROPN
ejpam-5611	4	10	and	and	CCONJ
ejpam-5611	4	11	the	the	DET
ejpam-5611	4	12	change	change	NOUN
ejpam-5611	4	13	of	of	ADP
ejpam-5611	4	14	variable	variable	ADJ
ejpam-5611	4	15	formula	formula	NOUN
ejpam-5611	4	16	for	for	ADP
ejpam-5611	4	17	the	the	DET
ejpam-5611	4	18	pu	pu	PROPN
ejpam-5611	4	19	integral	integral	ADJ
ejpam-5611	4	20	will	will	AUX
ejpam-5611	4	21	be	be	AUX
ejpam-5611	4	22	established	establish	VERB
ejpam-5611	4	23	.	.	PUNCT
ejpam-5611	5	1	2020	2020	NUM
ejpam-5611	5	2	mathematics	mathematic	NOUN
ejpam-5611	5	3	subject	subject	NOUN
ejpam-5611	5	4	classifications	classification	NOUN
ejpam-5611	5	5	:	:	PUNCT
ejpam-5611	5	6	28b05	28b05	NUM
ejpam-5611	5	7	,	,	PUNCT
ejpam-5611	5	8	26a39	26a39	NUM
ejpam-5611	5	9	,	,	PUNCT
ejpam-5611	5	10	32c09	32c09	NUM
ejpam-5611	5	11	key	key	ADJ
ejpam-5611	5	12	words	word	NOUN
ejpam-5611	5	13	and	and	CCONJ
ejpam-5611	5	14	phrases	phrase	NOUN
ejpam-5611	5	15	:	:	PUNCT
ejpam-5611	5	16	gauge	gauge	NOUN
ejpam-5611	5	17	integrals	integral	NOUN
ejpam-5611	5	18	,	,	PUNCT
ejpam-5611	5	19	partition	partition	NOUN
ejpam-5611	5	20	of	of	ADP
ejpam-5611	5	21	unity	unity	NOUN
ejpam-5611	5	22	,	,	PUNCT
ejpam-5611	5	23	change	change	NOUN
ejpam-5611	5	24	of	of	ADP
ejpam-5611	5	25	variable	variable	ADJ
ejpam-5611	5	26	formula	formula	NOUN
ejpam-5611	5	27	,	,	PUNCT
ejpam-5611	5	28	saks	sak	NOUN
ejpam-5611	5	29	-	-	PUNCT
ejpam-5611	5	30	henstock	henstock	NOUN
ejpam-5611	5	31	1	1	NUM
ejpam-5611	5	32	.	.	PUNCT
ejpam-5611	6	1	introduction	introduction	NOUN
ejpam-5611	6	2	henstock	henstock	PROPN
ejpam-5611	6	3	integral	integral	ADJ
ejpam-5611	6	4	is	be	AUX
ejpam-5611	6	5	an	an	DET
ejpam-5611	6	6	integration	integration	NOUN
ejpam-5611	6	7	process	process	NOUN
ejpam-5611	6	8	that	that	PRON
ejpam-5611	6	9	is	be	AUX
ejpam-5611	6	10	anchored	anchor	VERB
ejpam-5611	6	11	on	on	ADP
ejpam-5611	6	12	how	how	SCONJ
ejpam-5611	6	13	the	the	DET
ejpam-5611	6	14	riemann	riemann	PROPN
ejpam-5611	6	15	integral	integral	NOUN
ejpam-5611	6	16	is	be	AUX
ejpam-5611	6	17	constructed	construct	VERB
ejpam-5611	6	18	.	.	PUNCT
ejpam-5611	7	1	more	more	ADV
ejpam-5611	7	2	precisely	precisely	ADV
ejpam-5611	7	3	,	,	PUNCT
ejpam-5611	7	4	in	in	ADP
ejpam-5611	7	5	most	most	ADJ
ejpam-5611	7	6	cases	case	NOUN
ejpam-5611	7	7	,	,	PUNCT
ejpam-5611	7	8	it	it	PRON
ejpam-5611	7	9	is	be	AUX
ejpam-5611	7	10	more	more	ADV
ejpam-5611	7	11	general	general	ADJ
ejpam-5611	7	12	than	than	ADP
ejpam-5611	7	13	the	the	DET
ejpam-5611	7	14	lebesgue	lebesgue	NOUN
ejpam-5611	7	15	integral	integral	ADJ
ejpam-5611	7	16	and	and	CCONJ
ejpam-5611	7	17	its	its	PRON
ejpam-5611	7	18	construction	construction	NOUN
ejpam-5611	7	19	is	be	AUX
ejpam-5611	7	20	free	free	ADJ
ejpam-5611	7	21	from	from	ADP
ejpam-5611	7	22	a	a	DET
ejpam-5611	7	23	measure	measure	NOUN
ejpam-5611	7	24	theoretic	theoretic	ADJ
ejpam-5611	7	25	standpoint	standpoint	NOUN
ejpam-5611	7	26	.	.	PUNCT
ejpam-5611	8	1	thus	thus	ADV
ejpam-5611	8	2	,	,	PUNCT
ejpam-5611	8	3	it	it	PRON
ejpam-5611	8	4	is	be	AUX
ejpam-5611	8	5	,	,	PUNCT
ejpam-5611	8	6	relatively	relatively	ADV
ejpam-5611	8	7	,	,	PUNCT
ejpam-5611	8	8	easier	easy	ADJ
ejpam-5611	8	9	than	than	ADP
ejpam-5611	8	10	how	how	SCONJ
ejpam-5611	8	11	the	the	DET
ejpam-5611	8	12	lebesgue	lebesgue	ADJ
ejpam-5611	8	13	integral	integral	ADJ
ejpam-5611	8	14	was	be	AUX
ejpam-5611	8	15	constructed	construct	VERB
ejpam-5611	8	16	.	.	PUNCT
ejpam-5611	9	1	its	its	PRON
ejpam-5611	9	2	definition	definition	NOUN
ejpam-5611	9	3	is	be	AUX
ejpam-5611	9	4	through	through	ADP
ejpam-5611	9	5	a	a	DET
ejpam-5611	9	6	covering	covering	NOUN
ejpam-5611	9	7	system	system	NOUN
ejpam-5611	9	8	called	call	VERB
ejpam-5611	9	9	δ	δ	PROPN
ejpam-5611	9	10	-	-	PUNCT
ejpam-5611	9	11	fine	fine	NOUN
ejpam-5611	9	12	,	,	PUNCT
ejpam-5611	9	13	where	where	SCONJ
ejpam-5611	9	14	δ	δ	PROPN
ejpam-5611	9	15	is	be	AUX
ejpam-5611	9	16	a	a	DET
ejpam-5611	9	17	postive	postive	ADJ
ejpam-5611	9	18	function	function	NOUN
ejpam-5611	9	19	.	.	PUNCT
ejpam-5611	10	1	a	a	DET
ejpam-5611	10	2	number	number	NOUN
ejpam-5611	10	3	of	of	ADP
ejpam-5611	10	4	its	its	PRON
ejpam-5611	10	5	variants	variant	NOUN
ejpam-5611	10	6	were	be	AUX
ejpam-5611	10	7	established	establish	VERB
ejpam-5611	10	8	and	and	CCONJ
ejpam-5611	10	9	one	one	NUM
ejpam-5611	10	10	of	of	ADP
ejpam-5611	10	11	those	those	PRON
ejpam-5611	10	12	is	be	AUX
ejpam-5611	10	13	the	the	DET
ejpam-5611	10	14	pu	pu	PROPN
ejpam-5611	10	15	integral	integral	ADJ
ejpam-5611	10	16	,	,	PUNCT
ejpam-5611	10	17	a	a	DET
ejpam-5611	10	18	gauge	gauge	ADJ
ejpam-5611	10	19	type	type	NOUN
ejpam-5611	10	20	of	of	ADP
ejpam-5611	10	21	definition	definition	NOUN
ejpam-5611	10	22	that	that	PRON
ejpam-5611	10	23	is	be	AUX
ejpam-5611	10	24	anchored	anchor	VERB
ejpam-5611	10	25	in	in	ADP
ejpam-5611	10	26	the	the	DET
ejpam-5611	10	27	perspective	perspective	NOUN
ejpam-5611	10	28	of	of	ADP
ejpam-5611	10	29	a	a	DET
ejpam-5611	10	30	covering	covering	NOUN
ejpam-5611	10	31	systems	system	NOUN
ejpam-5611	10	32	though	though	SCONJ
ejpam-5611	10	33	partitions	partition	NOUN
ejpam-5611	10	34	of	of	ADP
ejpam-5611	10	35	unity	unity	NOUN
ejpam-5611	10	36	.	.	PUNCT
ejpam-5611	11	1	in	in	ADP
ejpam-5611	11	2	fact	fact	NOUN
ejpam-5611	11	3	,	,	PUNCT
ejpam-5611	11	4	[	[	X
ejpam-5611	11	5	1	1	X
ejpam-5611	11	6	]	]	PUNCT
ejpam-5611	11	7	mentioned	mention	VERB
ejpam-5611	11	8	that	that	SCONJ
ejpam-5611	11	9	the	the	DET
ejpam-5611	11	10	pu	pu	PROPN
ejpam-5611	11	11	integral	integral	ADJ
ejpam-5611	11	12	can	can	AUX
ejpam-5611	11	13	be	be	AUX
ejpam-5611	11	14	used	use	VERB
ejpam-5611	11	15	in	in	ADP
ejpam-5611	11	16	the	the	DET
ejpam-5611	11	17	integration	integration	NOUN
ejpam-5611	11	18	of	of	ADP
ejpam-5611	11	19	functions	function	NOUN
ejpam-5611	11	20	on	on	ADP
ejpam-5611	11	21	manifolds	manifold	NOUN
ejpam-5611	11	22	.	.	PUNCT
ejpam-5611	12	1	in	in	ADP
ejpam-5611	12	2	[	[	X
ejpam-5611	12	3	2	2	NUM
ejpam-5611	12	4	,	,	PUNCT
ejpam-5611	12	5	3	3	NUM
ejpam-5611	12	6	]	]	PUNCT
ejpam-5611	12	7	,	,	PUNCT
ejpam-5611	12	8	a	a	DET
ejpam-5611	12	9	henstock	henstock	NOUN
ejpam-5611	12	10	-	-	PUNCT
ejpam-5611	12	11	kurzweil	kurzweil	NOUN
ejpam-5611	12	12	integral	integral	ADJ
ejpam-5611	12	13	type	type	NOUN
ejpam-5611	12	14	were	be	AUX
ejpam-5611	12	15	established	establish	VERB
ejpam-5611	12	16	and	and	CCONJ
ejpam-5611	12	17	their	their	PRON
ejpam-5611	12	18	application	application	NOUN
ejpam-5611	12	19	to	to	ADP
ejpam-5611	12	20	functions	function	NOUN
ejpam-5611	12	21	on	on	ADP
ejpam-5611	12	22	manifolds	manifold	NOUN
ejpam-5611	12	23	were	be	AUX
ejpam-5611	12	24	presented	present	VERB
ejpam-5611	12	25	.	.	PUNCT
ejpam-5611	13	1	a	a	DET
ejpam-5611	13	2	finite	finite	ADJ
ejpam-5611	13	3	collection	collection	NOUN
ejpam-5611	13	4	of	of	ADP
ejpam-5611	13	5	point	point	NOUN
ejpam-5611	13	6	-	-	PUNCT
ejpam-5611	13	7	interval	interval	NOUN
ejpam-5611	13	8	pair	pair	NOUN
ejpam-5611	13	9	{	{	PUNCT
ejpam-5611	13	10	(	(	PUNCT
ejpam-5611	13	11	ti	ti	NOUN
ejpam-5611	13	12	,	,	PUNCT
ejpam-5611	13	13	ii)}mi=1	ii)}mi=1	PROPN
ejpam-5611	13	14	,	,	PUNCT
ejpam-5611	13	15	where	where	SCONJ
ejpam-5611	13	16	ii	ii	PROPN
ejpam-5611	13	17	is	be	AUX
ejpam-5611	13	18	a	a	DET
ejpam-5611	13	19	compact	compact	ADJ
ejpam-5611	13	20	interval	interval	NOUN
ejpam-5611	13	21	,	,	PUNCT
ejpam-5611	13	22	is	be	AUX
ejpam-5611	13	23	of	of	ADP
ejpam-5611	13	24	perron	perron	PROPN
ejpam-5611	13	25	type	type	NOUN
ejpam-5611	13	26	if	if	SCONJ
ejpam-5611	13	27	ti	ti	PROPN
ejpam-5611	13	28	∈	∈	PROPN
ejpam-5611	13	29	ii	ii	PROPN
ejpam-5611	13	30	for	for	ADP
ejpam-5611	13	31	all	all	DET
ejpam-5611	13	32	i	i	PRON
ejpam-5611	13	33	≤	≤	NUM
ejpam-5611	13	34	m.	m.	NOUN
ejpam-5611	13	35	for	for	ADP
ejpam-5611	13	36	a	a	DET
ejpam-5611	13	37	subset	subset	NOUN
ejpam-5611	13	38	e	e	NOUN
ejpam-5611	13	39	of	of	ADP
ejpam-5611	13	40	rn	rn	PROPN
ejpam-5611	13	41	,	,	PUNCT
ejpam-5611	13	42	the	the	DET
ejpam-5611	13	43	support	support	NOUN
ejpam-5611	13	44	of	of	ADP
ejpam-5611	13	45	a	a	DET
ejpam-5611	13	46	real	real	ADV
ejpam-5611	13	47	-	-	PUNCT
ejpam-5611	13	48	valued	value	VERB
ejpam-5611	13	49	∗corresponding	∗corresponding	NOUN
ejpam-5611	13	50	author	author	NOUN
ejpam-5611	13	51	.	.	PUNCT
ejpam-5611	14	1	doi	doi	NOUN
ejpam-5611	14	2	:	:	PUNCT
ejpam-5611	14	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5611	https://doi.org/10.29020/nybg.ejpam.v18i2.5611	ADJ
ejpam-5611	14	4	email	email	NOUN
ejpam-5611	14	5	addresses	address	NOUN
ejpam-5611	14	6	:	:	PUNCT
ejpam-5611	14	7	greigbates.flores@cmu.edu.ph	greigbates.flores@cmu.edu.ph	PROPN
ejpam-5611	14	8	(	(	PUNCT
ejpam-5611	14	9	g.	g.	PROPN
ejpam-5611	14	10	flores	flores	PROPN
ejpam-5611	14	11	)	)	PUNCT
ejpam-5611	14	12	,	,	PUNCT
ejpam-5611	14	13	f.annleslie.flores@cmu.edu.ph	f.annleslie.flores@cmu.edu.ph	PROPN
ejpam-5611	14	14	(	(	PUNCT
ejpam-5611	14	15	a.	a.	NOUN
ejpam-5611	14	16	flores	flores	PROPN
ejpam-5611	14	17	)	)	PUNCT
ejpam-5611	14	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5611	15	1	1	1	NUM
ejpam-5611	15	2	copyright	copyright	NOUN
ejpam-5611	15	3	:	:	PUNCT
ejpam-5611	15	4	©	©	PROPN
ejpam-5611	15	5	2025	2025	NUM
ejpam-5611	15	6	the	the	DET
ejpam-5611	15	7	author(s	author(s	NOUN
ejpam-5611	15	8	)	)	PUNCT
ejpam-5611	15	9	.	.	PUNCT
ejpam-5611	16	1	(	(	PUNCT
ejpam-5611	16	2	cc	cc	NOUN
ejpam-5611	16	3	by	by	ADP
ejpam-5611	16	4	-	-	PUNCT
ejpam-5611	16	5	nc	nc	PROPN
ejpam-5611	16	6	4.0	4.0	NUM
ejpam-5611	16	7	)	)	PUNCT
ejpam-5611	16	8	g.	g.	PROPN
ejpam-5611	16	9	flores	flores	PROPN
ejpam-5611	16	10	,	,	PUNCT
ejpam-5611	16	11	a.	a.	PROPN
ejpam-5611	16	12	flores	flores	PROPN
ejpam-5611	16	13	/	/	SYM
ejpam-5611	16	14	eur	eur	PROPN
ejpam-5611	16	15	.	.	PUNCT
ejpam-5611	17	1	j.	j.	PROPN
ejpam-5611	17	2	pure	pure	PROPN
ejpam-5611	17	3	appl	appl	PROPN
ejpam-5611	17	4	.	.	PROPN
ejpam-5611	17	5	math	math	PROPN
ejpam-5611	17	6	,	,	PUNCT
ejpam-5611	17	7	18	18	NUM
ejpam-5611	17	8	(	(	PUNCT
ejpam-5611	17	9	2	2	NUM
ejpam-5611	17	10	)	)	PUNCT
ejpam-5611	17	11	(	(	PUNCT
ejpam-5611	17	12	2025	2025	NUM
ejpam-5611	17	13	)	)	PUNCT
ejpam-5611	17	14	,	,	PUNCT
ejpam-5611	17	15	5611	5611	NUM
ejpam-5611	17	16	2	2	NUM
ejpam-5611	17	17	of	of	ADP
ejpam-5611	17	18	16	16	NUM
ejpam-5611	17	19	function	function	NOUN
ejpam-5611	17	20	f	f	PROPN
ejpam-5611	17	21	on	on	ADP
ejpam-5611	17	22	e	e	NOUN
ejpam-5611	17	23	,	,	PUNCT
ejpam-5611	17	24	written	write	VERB
ejpam-5611	17	25	as	as	ADP
ejpam-5611	17	26	suppf	suppf	NOUN
ejpam-5611	17	27	is	be	AUX
ejpam-5611	17	28	the	the	DET
ejpam-5611	17	29	closure	closure	NOUN
ejpam-5611	17	30	of	of	ADP
ejpam-5611	17	31	the	the	DET
ejpam-5611	17	32	set	set	NOUN
ejpam-5611	17	33	of	of	ADP
ejpam-5611	17	34	points	point	NOUN
ejpam-5611	17	35	in	in	ADP
ejpam-5611	17	36	the	the	DET
ejpam-5611	17	37	domain	domain	NOUN
ejpam-5611	17	38	whose	whose	DET
ejpam-5611	17	39	image	image	NOUN
ejpam-5611	17	40	under	under	ADP
ejpam-5611	17	41	f	f	PROPN
ejpam-5611	17	42	is	be	AUX
ejpam-5611	17	43	nonzero	nonzero	NOUN
ejpam-5611	17	44	.	.	PUNCT
ejpam-5611	18	1	moreover	moreover	ADV
ejpam-5611	18	2	,	,	PUNCT
ejpam-5611	18	3	given	give	VERB
ejpam-5611	18	4	a	a	DET
ejpam-5611	18	5	gauge	gauge	ADJ
ejpam-5611	18	6	δ	δ	NOUN
ejpam-5611	18	7	on	on	ADP
ejpam-5611	18	8	[	[	X
ejpam-5611	18	9	a	a	X
ejpam-5611	18	10	,	,	PUNCT
ejpam-5611	18	11	b	b	NOUN
ejpam-5611	18	12	]	]	X
ejpam-5611	18	13	,	,	PUNCT
ejpam-5611	18	14	a	a	DET
ejpam-5611	18	15	finite	finite	ADJ
ejpam-5611	18	16	collection	collection	NOUN
ejpam-5611	18	17	of	of	ADP
ejpam-5611	18	18	point	point	NOUN
ejpam-5611	18	19	interval	interval	NOUN
ejpam-5611	18	20	pairs	pair	NOUN
ejpam-5611	18	21	,	,	PUNCT
ejpam-5611	18	22	of	of	ADP
ejpam-5611	18	23	perron	perron	PROPN
ejpam-5611	18	24	type	type	NOUN
ejpam-5611	18	25	,	,	PUNCT
ejpam-5611	18	26	{	{	PUNCT
ejpam-5611	18	27	(	(	PUNCT
ejpam-5611	18	28	ti	ti	NOUN
ejpam-5611	18	29	,	,	PUNCT
ejpam-5611	18	30	ii)}mi=1	ii)}mi=1	PROPN
ejpam-5611	18	31	is	be	AUX
ejpam-5611	18	32	said	say	VERB
ejpam-5611	18	33	to	to	PART
ejpam-5611	18	34	be	be	AUX
ejpam-5611	18	35	δ	δ	NOUN
ejpam-5611	18	36	-	-	ADJ
ejpam-5611	18	37	fine	fine	ADJ
ejpam-5611	18	38	perron	perron	PROPN
ejpam-5611	18	39	partition	partition	NOUN
ejpam-5611	18	40	of	of	ADP
ejpam-5611	18	41	[	[	X
ejpam-5611	18	42	a	a	X
ejpam-5611	18	43	,	,	PUNCT
ejpam-5611	18	44	b	b	NOUN
ejpam-5611	18	45	]	]	X
ejpam-5611	18	46	if	if	SCONJ
ejpam-5611	18	47	ii	ii	PROPN
ejpam-5611	18	48	is	be	AUX
ejpam-5611	18	49	a	a	DET
ejpam-5611	18	50	partition	partition	NOUN
ejpam-5611	18	51	of	of	ADP
ejpam-5611	18	52	[	[	X
ejpam-5611	18	53	a	a	X
ejpam-5611	18	54	,	,	PUNCT
ejpam-5611	18	55	b	b	NOUN
ejpam-5611	18	56	]	]	PUNCT
ejpam-5611	18	57	and	and	CCONJ
ejpam-5611	18	58	ii	ii	PROPN
ejpam-5611	18	59	⊆	⊆	NUM
ejpam-5611	18	60	b(ti	b(ti	NOUN
ejpam-5611	18	61	,	,	PUNCT
ejpam-5611	18	62	δ(ti	δ(ti	NOUN
ejpam-5611	18	63	)	)	PUNCT
ejpam-5611	18	64	)	)	PUNCT
ejpam-5611	18	65	.	.	PUNCT
ejpam-5611	19	1	if	if	SCONJ
ejpam-5611	19	2	for	for	ADP
ejpam-5611	19	3	each	each	DET
ejpam-5611	19	4	i	i	NOUN
ejpam-5611	19	5	≤	≤	PROPN
ejpam-5611	19	6	m	m	ADP
ejpam-5611	19	7	,	,	PUNCT
ejpam-5611	19	8	the	the	DET
ejpam-5611	19	9	condition	condition	NOUN
ejpam-5611	19	10	ti	ti	PROPN
ejpam-5611	19	11	∈	∈	PROPN
ejpam-5611	19	12	ii	ii	NOUN
ejpam-5611	19	13	is	be	AUX
ejpam-5611	19	14	removed	remove	VERB
ejpam-5611	19	15	,	,	PUNCT
ejpam-5611	19	16	then	then	ADV
ejpam-5611	19	17	we	we	PRON
ejpam-5611	19	18	obtain	obtain	VERB
ejpam-5611	19	19	the	the	DET
ejpam-5611	19	20	mcshane	mcshane	NOUN
ejpam-5611	19	21	integral	integral	PROPN
ejpam-5611	19	22	.	.	PUNCT
ejpam-5611	20	1	on	on	ADP
ejpam-5611	20	2	another	another	DET
ejpam-5611	20	3	note	note	NOUN
ejpam-5611	20	4	,	,	PUNCT
ejpam-5611	20	5	a	a	DET
ejpam-5611	20	6	partition	partition	NOUN
ejpam-5611	20	7	of	of	ADP
ejpam-5611	20	8	unity	unity	NOUN
ejpam-5611	20	9	[	[	X
ejpam-5611	20	10	1	1	NUM
ejpam-5611	20	11	,	,	PUNCT
ejpam-5611	20	12	2	2	NUM
ejpam-5611	20	13	]	]	PUNCT
ejpam-5611	20	14	on	on	ADP
ejpam-5611	20	15	a	a	DET
ejpam-5611	20	16	compact	compact	ADJ
ejpam-5611	20	17	interval	interval	NOUN
ejpam-5611	20	18	e	e	NOUN
ejpam-5611	20	19	⊆	⊆	NUM
ejpam-5611	20	20	rn	rn	PROPN
ejpam-5611	20	21	is	be	AUX
ejpam-5611	20	22	a	a	DET
ejpam-5611	20	23	finite	finite	ADJ
ejpam-5611	20	24	collection	collection	NOUN
ejpam-5611	20	25	{	{	PUNCT
ejpam-5611	20	26	φi}mi=1	φi}mi=1	VERB
ejpam-5611	20	27	smooth	smooth	ADJ
ejpam-5611	20	28	functions	function	NOUN
ejpam-5611	20	29	with	with	ADP
ejpam-5611	20	30	the	the	DET
ejpam-5611	20	31	following	follow	VERB
ejpam-5611	20	32	conditions	condition	NOUN
ejpam-5611	20	33	:	:	PUNCT
ejpam-5611	20	34	(	(	PUNCT
ejpam-5611	20	35	i	i	NOUN
ejpam-5611	20	36	)	)	PUNCT
ejpam-5611	20	37	φi	φi	ADP
ejpam-5611	20	38	≥	≥	NOUN
ejpam-5611	20	39	0	0	NUM
ejpam-5611	20	40	on	on	ADP
ejpam-5611	20	41	e	e	NOUN
ejpam-5611	20	42	;	;	PUNCT
ejpam-5611	20	43	(	(	PUNCT
ejpam-5611	20	44	ii	ii	NOUN
ejpam-5611	20	45	)	)	PUNCT
ejpam-5611	20	46	m∑	m∑	VERB
ejpam-5611	20	47	k=1	k=1	NOUN
ejpam-5611	20	48	φk	φk	ADP
ejpam-5611	20	49	=	=	SYM
ejpam-5611	20	50	1	1	NUM
ejpam-5611	20	51	a.e	a.e	PROPN
ejpam-5611	20	52	.	.	PROPN
ejpam-5611	21	1	on	on	ADP
ejpam-5611	21	2	e.	e.	PROPN
ejpam-5611	22	1	if	if	SCONJ
ejpam-5611	22	2	m∑	m∑	PRON
ejpam-5611	22	3	k=1	k=1	X
ejpam-5611	22	4	φk	φk	ADP
ejpam-5611	22	5	≤	≤	NUM
ejpam-5611	22	6	1	1	NUM
ejpam-5611	22	7	a.e	a.e	PROPN
ejpam-5611	22	8	.	.	PROPN
ejpam-5611	23	1	on	on	ADP
ejpam-5611	23	2	e	e	NOUN
ejpam-5611	23	3	,	,	PUNCT
ejpam-5611	23	4	then	then	ADV
ejpam-5611	23	5	{	{	PUNCT
ejpam-5611	23	6	φi}mi=1	φi}mi=1	PROPN
ejpam-5611	23	7	is	be	AUX
ejpam-5611	23	8	said	say	VERB
ejpam-5611	23	9	to	to	PART
ejpam-5611	23	10	be	be	AUX
ejpam-5611	23	11	a	a	DET
ejpam-5611	23	12	partial	partial	ADJ
ejpam-5611	23	13	partition	partition	NOUN
ejpam-5611	23	14	of	of	ADP
ejpam-5611	23	15	unity	unity	NOUN
ejpam-5611	23	16	.	.	PUNCT
ejpam-5611	24	1	a	a	DET
ejpam-5611	24	2	finite	finite	ADJ
ejpam-5611	24	3	collection	collection	NOUN
ejpam-5611	24	4	of	of	ADP
ejpam-5611	24	5	triples	triple	NOUN
ejpam-5611	24	6	{	{	PUNCT
ejpam-5611	24	7	(	(	PUNCT
ejpam-5611	24	8	ξi	ξi	NOUN
ejpam-5611	24	9	,	,	PUNCT
ejpam-5611	24	10	ii	ii	PROPN
ejpam-5611	24	11	,	,	PUNCT
ejpam-5611	24	12	φ)}mi=1	φ)}mi=1	AUX
ejpam-5611	24	13	is	be	AUX
ejpam-5611	24	14	said	say	VERB
ejpam-5611	24	15	to	to	PART
ejpam-5611	24	16	be	be	AUX
ejpam-5611	24	17	δ	δ	PROPN
ejpam-5611	24	18	-	-	PUNCT
ejpam-5611	24	19	fine	fine	ADJ
ejpam-5611	24	20	pu	pu	PROPN
ejpam-5611	24	21	-	-	NOUN
ejpam-5611	24	22	division	division	NOUN
ejpam-5611	24	23	of	of	ADP
ejpam-5611	24	24	e	e	PRON
ejpam-5611	24	25	if	if	SCONJ
ejpam-5611	24	26	for	for	ADP
ejpam-5611	24	27	each	each	DET
ejpam-5611	24	28	i	i	PROPN
ejpam-5611	24	29	≤	≤	PROPN
ejpam-5611	24	30	m	m	ADP
ejpam-5611	24	31	,	,	PUNCT
ejpam-5611	24	32	supp	supp	PROPN
ejpam-5611	24	33	φi	φi	ADP
ejpam-5611	24	34	⊆	⊆	NUM
ejpam-5611	24	35	ii	ii	NOUN
ejpam-5611	24	36	and	and	CCONJ
ejpam-5611	24	37	ii	ii	PROPN
ejpam-5611	24	38	⊆	⊆	NUM
ejpam-5611	24	39	b(ξi	b(ξi	NOUN
ejpam-5611	24	40	,	,	PUNCT
ejpam-5611	24	41	δ(ξi	δ(ξi	ADP
ejpam-5611	24	42	)	)	PUNCT
ejpam-5611	24	43	)	)	PUNCT
ejpam-5611	24	44	.	.	PUNCT
ejpam-5611	25	1	boonpogkrong	boonpogkrong	PROPN
ejpam-5611	25	2	,	,	PUNCT
ejpam-5611	25	3	revisited	revisit	VERB
ejpam-5611	25	4	the	the	DET
ejpam-5611	25	5	notion	notion	NOUN
ejpam-5611	25	6	of	of	ADP
ejpam-5611	25	7	the	the	DET
ejpam-5611	25	8	pul	pul	NOUN
ejpam-5611	25	9	integral	integral	ADJ
ejpam-5611	25	10	and	and	CCONJ
ejpam-5611	25	11	it	it	PRON
ejpam-5611	25	12	’s	’	VERB
ejpam-5611	25	13	application	application	NOUN
ejpam-5611	25	14	in	in	ADP
ejpam-5611	25	15	the	the	DET
ejpam-5611	25	16	integrals	integral	NOUN
ejpam-5611	25	17	of	of	ADP
ejpam-5611	25	18	a	a	DET
ejpam-5611	25	19	function	function	NOUN
ejpam-5611	25	20	defined	define	VERB
ejpam-5611	25	21	on	on	ADP
ejpam-5611	25	22	a	a	DET
ejpam-5611	25	23	manifold	manifold	NOUN
ejpam-5611	25	24	.	.	PUNCT
ejpam-5611	26	1	moreover	moreover	ADV
ejpam-5611	26	2	,	,	PUNCT
ejpam-5611	26	3	flores	flore	NOUN
ejpam-5611	26	4	and	and	CCONJ
ejpam-5611	26	5	benitez	benitez	PROPN
ejpam-5611	27	1	[	[	X
ejpam-5611	27	2	4	4	NUM
ejpam-5611	27	3	,	,	PUNCT
ejpam-5611	27	4	5	5	NUM
ejpam-5611	27	5	]	]	PUNCT
ejpam-5611	27	6	generalizes	generalize	VERB
ejpam-5611	27	7	the	the	DET
ejpam-5611	27	8	notion	notion	NOUN
ejpam-5611	27	9	in	in	ADP
ejpam-5611	27	10	its	its	PRON
ejpam-5611	27	11	stieltjes	stieltjes	NOUN
ejpam-5611	27	12	form	form	NOUN
ejpam-5611	27	13	and	and	CCONJ
ejpam-5611	27	14	establsihed	establsihe	VERB
ejpam-5611	27	15	some	some	DET
ejpam-5611	27	16	convergence	convergence	NOUN
ejpam-5611	27	17	theorems	theorem	NOUN
ejpam-5611	27	18	.	.	PUNCT
ejpam-5611	28	1	in	in	ADP
ejpam-5611	28	2	this	this	DET
ejpam-5611	28	3	paper	paper	NOUN
ejpam-5611	28	4	,	,	PUNCT
ejpam-5611	28	5	the	the	DET
ejpam-5611	28	6	definition	definition	NOUN
ejpam-5611	28	7	of	of	ADP
ejpam-5611	28	8	the	the	DET
ejpam-5611	28	9	pu	pu	PROPN
ejpam-5611	28	10	integral	integral	ADJ
ejpam-5611	28	11	will	will	AUX
ejpam-5611	28	12	be	be	AUX
ejpam-5611	28	13	discussed	discuss	VERB
ejpam-5611	28	14	and	and	CCONJ
ejpam-5611	28	15	the	the	DET
ejpam-5611	28	16	change	change	NOUN
ejpam-5611	28	17	of	of	ADP
ejpam-5611	28	18	variable	variable	ADJ
ejpam-5611	28	19	formula	formula	NOUN
ejpam-5611	28	20	and	and	CCONJ
ejpam-5611	28	21	the	the	DET
ejpam-5611	28	22	saks	sak	NOUN
ejpam-5611	28	23	-	-	PUNCT
ejpam-5611	28	24	henstock	henstock	NOUN
ejpam-5611	28	25	lemma	lemma	PROPN
ejpam-5611	28	26	of	of	ADP
ejpam-5611	28	27	this	this	DET
ejpam-5611	28	28	integral	integral	ADJ
ejpam-5611	28	29	will	will	AUX
ejpam-5611	28	30	be	be	AUX
ejpam-5611	28	31	established	establish	VERB
ejpam-5611	28	32	.	.	PUNCT
ejpam-5611	29	1	2	2	X
ejpam-5611	29	2	.	.	NUM
ejpam-5611	29	3	preliminaries	preliminary	NOUN
ejpam-5611	29	4	in	in	ADP
ejpam-5611	29	5	this	this	DET
ejpam-5611	29	6	section	section	NOUN
ejpam-5611	29	7	,	,	PUNCT
ejpam-5611	29	8	we	we	PRON
ejpam-5611	29	9	introduce	introduce	VERB
ejpam-5611	29	10	the	the	DET
ejpam-5611	29	11	pu	pu	PROPN
ejpam-5611	29	12	integral	integral	NOUN
ejpam-5611	29	13	of	of	ADP
ejpam-5611	29	14	a	a	DET
ejpam-5611	29	15	function	function	NOUN
ejpam-5611	29	16	defined	define	VERB
ejpam-5611	29	17	on	on	ADP
ejpam-5611	29	18	a	a	DET
ejpam-5611	29	19	manifold	manifold	NOUN
ejpam-5611	29	20	.	.	PUNCT
ejpam-5611	30	1	throughout	throughout	ADP
ejpam-5611	30	2	the	the	DET
ejpam-5611	30	3	rest	rest	NOUN
ejpam-5611	30	4	of	of	ADP
ejpam-5611	30	5	this	this	DET
ejpam-5611	30	6	chapter	chapter	NOUN
ejpam-5611	30	7	,	,	PUNCT
ejpam-5611	30	8	if	if	SCONJ
ejpam-5611	30	9	no	no	DET
ejpam-5611	30	10	confusion	confusion	NOUN
ejpam-5611	30	11	arises	arise	VERB
ejpam-5611	30	12	,	,	PUNCT
ejpam-5611	30	13	we	we	PRON
ejpam-5611	30	14	denote	denote	VERB
ejpam-5611	30	15	m	m	PROPN
ejpam-5611	30	16	as	as	ADP
ejpam-5611	30	17	a	a	DET
ejpam-5611	30	18	manifold	manifold	NOUN
ejpam-5611	30	19	.	.	PUNCT
ejpam-5611	31	1	definition	definition	NOUN
ejpam-5611	31	2	1	1	NUM
ejpam-5611	31	3	.	.	PUNCT
ejpam-5611	32	1	[	[	X
ejpam-5611	32	2	3	3	NUM
ejpam-5611	32	3	,	,	PUNCT
ejpam-5611	32	4	4	4	NUM
ejpam-5611	32	5	]	]	PUNCT
ejpam-5611	32	6	let	let	VERB
ejpam-5611	32	7	x	x	PRON
ejpam-5611	32	8	be	be	AUX
ejpam-5611	32	9	a	a	DET
ejpam-5611	32	10	banach	banach	NOUN
ejpam-5611	32	11	space	space	NOUN
ejpam-5611	32	12	and	and	CCONJ
ejpam-5611	32	13	let	let	VERB
ejpam-5611	32	14	f	f	NOUN
ejpam-5611	32	15	:	:	PUNCT
ejpam-5611	33	1	[	[	X
ejpam-5611	33	2	a	a	X
ejpam-5611	33	3	,	,	PUNCT
ejpam-5611	33	4	b	b	NOUN
ejpam-5611	33	5	]	]	X
ejpam-5611	33	6	→	→	PUNCT
ejpam-5611	33	7	x	x	X
ejpam-5611	33	8	.	.	PUNCT
ejpam-5611	34	1	we	we	PRON
ejpam-5611	34	2	define	define	VERB
ejpam-5611	34	3	the	the	DET
ejpam-5611	34	4	pu	pu	PROPN
ejpam-5611	34	5	sum	sum	NOUN
ejpam-5611	34	6	by	by	ADP
ejpam-5611	34	7	s(f	s(f	PROPN
ejpam-5611	34	8	,	,	PUNCT
ejpam-5611	34	9	d	d	NOUN
ejpam-5611	34	10	)	)	PUNCT
ejpam-5611	34	11	=	=	PUNCT
ejpam-5611	34	12	m∑	m∑	ADV
ejpam-5611	34	13	k=1	k=1	PROPN
ejpam-5611	34	14	f(ξk	f(ξk	PROPN
ejpam-5611	34	15	)	)	PUNCT
ejpam-5611	34	16	(	(	PUNCT
ejpam-5611	34	17	r	r	NOUN
ejpam-5611	34	18	)	)	PUNCT
ejpam-5611	34	19	∫	∫	PROPN
ejpam-5611	34	20	ik	ik	PROPN
ejpam-5611	34	21	φk	φk	ADP
ejpam-5611	34	22	where	where	SCONJ
ejpam-5611	34	23	d	d	NOUN
ejpam-5611	34	24	is	be	AUX
ejpam-5611	34	25	a	a	DET
ejpam-5611	34	26	δ	δ	NOUN
ejpam-5611	34	27	-	-	PUNCT
ejpam-5611	34	28	fine	fine	ADJ
ejpam-5611	34	29	division	division	NOUN
ejpam-5611	34	30	of	of	ADP
ejpam-5611	34	31	[	[	X
ejpam-5611	34	32	a	a	X
ejpam-5611	34	33	,	,	PUNCT
ejpam-5611	34	34	b	b	NOUN
ejpam-5611	34	35	]	]	PUNCT
ejpam-5611	34	36	and	and	CCONJ
ejpam-5611	34	37	(	(	PUNCT
ejpam-5611	34	38	r	r	NOUN
ejpam-5611	34	39	)	)	PUNCT
ejpam-5611	34	40	∫	∫	NOUN
ejpam-5611	35	1	ik	ik	PROPN
ejpam-5611	35	2	φk	φk	PROPN
ejpam-5611	35	3	is	be	AUX
ejpam-5611	35	4	the	the	DET
ejpam-5611	35	5	riemann	riemann	PROPN
ejpam-5611	35	6	integral	integral	NOUN
ejpam-5611	35	7	of	of	ADP
ejpam-5611	35	8	φk	φk	ADP
ejpam-5611	35	9	for	for	ADP
ejpam-5611	35	10	all	all	DET
ejpam-5611	35	11	k	k	PROPN
ejpam-5611	35	12	∈	∈	PROPN
ejpam-5611	35	13	{	{	PUNCT
ejpam-5611	35	14	1	1	NUM
ejpam-5611	35	15	,	,	PUNCT
ejpam-5611	35	16	2	2	NUM
ejpam-5611	35	17	,	,	PUNCT
ejpam-5611	35	18	·	·	PUNCT
ejpam-5611	35	19	·	·	PUNCT
ejpam-5611	35	20	·	·	PUNCT
ejpam-5611	35	21	m	m	X
ejpam-5611	35	22	}	}	PUNCT
ejpam-5611	35	23	.	.	PUNCT
ejpam-5611	36	1	for	for	ADP
ejpam-5611	36	2	brevity	brevity	NOUN
ejpam-5611	36	3	,	,	PUNCT
ejpam-5611	36	4	we	we	PRON
ejpam-5611	36	5	write	write	VERB
ejpam-5611	36	6	a	a	DET
ejpam-5611	36	7	δ	δ	NOUN
ejpam-5611	36	8	-	-	PUNCT
ejpam-5611	36	9	fine	fine	ADJ
ejpam-5611	36	10	division	division	NOUN
ejpam-5611	36	11	of	of	ADP
ejpam-5611	36	12	[	[	X
ejpam-5611	36	13	a	a	X
ejpam-5611	36	14	,	,	PUNCT
ejpam-5611	36	15	b	b	NOUN
ejpam-5611	36	16	]	]	PUNCT
ejpam-5611	36	17	by	by	ADP
ejpam-5611	36	18	d	d	PROPN
ejpam-5611	36	19	=	=	SYM
ejpam-5611	36	20	{	{	PUNCT
ejpam-5611	36	21	(	(	PUNCT
ejpam-5611	36	22	ξ	ξ	PROPN
ejpam-5611	36	23	,	,	PUNCT
ejpam-5611	36	24	i	i	PRON
ejpam-5611	36	25	,	,	PUNCT
ejpam-5611	36	26	ψ	ψ	NOUN
ejpam-5611	36	27	)	)	PUNCT
ejpam-5611	36	28	}	}	PUNCT
ejpam-5611	36	29	and	and	CCONJ
ejpam-5611	36	30	a	a	DET
ejpam-5611	36	31	pu	pu	PROPN
ejpam-5611	36	32	sum	sum	NOUN
ejpam-5611	36	33	of	of	ADP
ejpam-5611	36	34	f	f	PROPN
ejpam-5611	36	35	over	over	ADP
ejpam-5611	36	36	d	d	PROPN
ejpam-5611	36	37	by	by	ADP
ejpam-5611	36	38	s(f	s(f	PROPN
ejpam-5611	36	39	,	,	PUNCT
ejpam-5611	36	40	d	d	NOUN
ejpam-5611	36	41	)	)	PUNCT
ejpam-5611	36	42	=	=	SYM
ejpam-5611	37	1	(	(	PUNCT
ejpam-5611	37	2	d	d	NOUN
ejpam-5611	37	3	)	)	PUNCT
ejpam-5611	37	4	∑	∑	SYM
ejpam-5611	37	5	f(ξ	f(ξ	NOUN
ejpam-5611	37	6	)	)	PUNCT
ejpam-5611	37	7	∫	∫	NOUN
ejpam-5611	38	1	i	i	PRON
ejpam-5611	38	2	ψ	ψ	X
ejpam-5611	38	3	=	=	PUNCT
ejpam-5611	38	4	∑	∑	PROPN
ejpam-5611	38	5	d	d	PROPN
ejpam-5611	38	6	f(ξ	f(ξ	NOUN
ejpam-5611	38	7	)	)	PUNCT
ejpam-5611	38	8	∫	∫	NOUN
ejpam-5611	39	1	i	i	PRON
ejpam-5611	39	2	ψ	ψ	PROPN
ejpam-5611	39	3	.	.	PUNCT
ejpam-5611	40	1	g.	g.	PROPN
ejpam-5611	40	2	flores	flores	PROPN
ejpam-5611	40	3	,	,	PUNCT
ejpam-5611	40	4	a.	a.	PROPN
ejpam-5611	40	5	flores	flores	PROPN
ejpam-5611	40	6	/	/	SYM
ejpam-5611	40	7	eur	eur	PROPN
ejpam-5611	40	8	.	.	PUNCT
ejpam-5611	41	1	j.	j.	PROPN
ejpam-5611	41	2	pure	pure	PROPN
ejpam-5611	41	3	appl	appl	PROPN
ejpam-5611	41	4	.	.	PROPN
ejpam-5611	41	5	math	math	PROPN
ejpam-5611	41	6	,	,	PUNCT
ejpam-5611	41	7	18	18	NUM
ejpam-5611	41	8	(	(	PUNCT
ejpam-5611	41	9	2	2	NUM
ejpam-5611	41	10	)	)	PUNCT
ejpam-5611	41	11	(	(	PUNCT
ejpam-5611	41	12	2025	2025	NUM
ejpam-5611	41	13	)	)	PUNCT
ejpam-5611	41	14	,	,	PUNCT
ejpam-5611	41	15	5611	5611	NUM
ejpam-5611	41	16	3	3	NUM
ejpam-5611	41	17	of	of	ADP
ejpam-5611	41	18	16	16	NUM
ejpam-5611	41	19	definition	definition	NOUN
ejpam-5611	41	20	2	2	NUM
ejpam-5611	41	21	.	.	PUNCT
ejpam-5611	42	1	[	[	X
ejpam-5611	42	2	4	4	X
ejpam-5611	42	3	]	]	PUNCT
ejpam-5611	42	4	let	let	VERB
ejpam-5611	42	5	x	x	PRON
ejpam-5611	42	6	be	be	AUX
ejpam-5611	42	7	a	a	DET
ejpam-5611	42	8	banach	banach	NOUN
ejpam-5611	42	9	space	space	NOUN
ejpam-5611	42	10	and	and	CCONJ
ejpam-5611	42	11	f	f	NOUN
ejpam-5611	42	12	:	:	PUNCT
ejpam-5611	43	1	[	[	X
ejpam-5611	43	2	a	a	X
ejpam-5611	43	3	,	,	PUNCT
ejpam-5611	43	4	b	b	NOUN
ejpam-5611	43	5	]	]	X
ejpam-5611	43	6	→	→	PUNCT
ejpam-5611	43	7	x	x	PART
ejpam-5611	43	8	be	be	AUX
ejpam-5611	43	9	a	a	DET
ejpam-5611	43	10	banach	banach	ADV
ejpam-5611	43	11	-	-	PUNCT
ejpam-5611	43	12	valued	value	VERB
ejpam-5611	43	13	funtion	funtion	NOUN
ejpam-5611	43	14	.	.	PUNCT
ejpam-5611	44	1	we	we	PRON
ejpam-5611	44	2	say	say	VERB
ejpam-5611	44	3	that	that	SCONJ
ejpam-5611	44	4	f	f	PROPN
ejpam-5611	44	5	is	be	AUX
ejpam-5611	44	6	pu	pu	PROPN
ejpam-5611	44	7	integrable	integrable	ADJ
ejpam-5611	44	8	to	to	ADP
ejpam-5611	44	9	a	a	DET
ejpam-5611	44	10	vector	vector	NOUN
ejpam-5611	44	11	a	a	PRON
ejpam-5611	44	12	over	over	ADP
ejpam-5611	44	13	[	[	X
ejpam-5611	44	14	a	a	DET
ejpam-5611	44	15	,	,	PUNCT
ejpam-5611	44	16	b	b	NOUN
ejpam-5611	44	17	]	]	X
ejpam-5611	44	18	if	if	SCONJ
ejpam-5611	44	19	for	for	ADP
ejpam-5611	44	20	every	every	DET
ejpam-5611	44	21	ϵ	ϵ	X
ejpam-5611	44	22	>	>	X
ejpam-5611	44	23	0	0	NUM
ejpam-5611	44	24	,	,	PUNCT
ejpam-5611	44	25	there	there	PRON
ejpam-5611	44	26	exists	exist	VERB
ejpam-5611	44	27	a	a	DET
ejpam-5611	44	28	gauge	gauge	NOUN
ejpam-5611	44	29	δ	δ	NOUN
ejpam-5611	44	30	on	on	ADP
ejpam-5611	44	31	[	[	X
ejpam-5611	44	32	a	a	DET
ejpam-5611	44	33	,	,	PUNCT
ejpam-5611	44	34	b	b	NOUN
ejpam-5611	44	35	]	]	X
ejpam-5611	44	36	such	such	ADJ
ejpam-5611	44	37	that	that	PRON
ejpam-5611	44	38	for	for	ADP
ejpam-5611	44	39	every	every	DET
ejpam-5611	44	40	δ	δ	PROPN
ejpam-5611	44	41	-	-	PUNCT
ejpam-5611	44	42	fine	fine	ADJ
ejpam-5611	44	43	division	division	NOUN
ejpam-5611	44	44	d	d	NOUN
ejpam-5611	44	45	of	of	ADP
ejpam-5611	44	46	[	[	X
ejpam-5611	44	47	a	a	X
ejpam-5611	44	48	,	,	PUNCT
ejpam-5611	44	49	b	b	NOUN
ejpam-5611	44	50	]	]	X
ejpam-5611	44	51	,	,	PUNCT
ejpam-5611	44	52	we	we	PRON
ejpam-5611	44	53	have	have	VERB
ejpam-5611	44	54	∥s(f	∥s(f	ADJ
ejpam-5611	44	55	,	,	PUNCT
ejpam-5611	44	56	d)−a∥	d)−a∥	NOUN
ejpam-5611	44	57	<	<	X
ejpam-5611	44	58	ϵ.	ϵ.	NOUN
ejpam-5611	45	1	if	if	SCONJ
ejpam-5611	45	2	a	a	PRON
ejpam-5611	45	3	is	be	AUX
ejpam-5611	45	4	the	the	DET
ejpam-5611	45	5	pu	pu	PROPN
ejpam-5611	45	6	integral	integral	ADJ
ejpam-5611	45	7	of	of	ADP
ejpam-5611	45	8	f	f	PROPN
ejpam-5611	45	9	with	with	ADP
ejpam-5611	45	10	over	over	ADP
ejpam-5611	45	11	[	[	X
ejpam-5611	45	12	a	a	DET
ejpam-5611	45	13	,	,	PUNCT
ejpam-5611	45	14	b	b	NOUN
ejpam-5611	45	15	]	]	X
ejpam-5611	45	16	,	,	PUNCT
ejpam-5611	45	17	then	then	ADV
ejpam-5611	45	18	we	we	PRON
ejpam-5611	45	19	write	write	VERB
ejpam-5611	45	20	a	a	DET
ejpam-5611	45	21	=	=	X
ejpam-5611	45	22	(	(	PUNCT
ejpam-5611	45	23	p	p	NOUN
ejpam-5611	45	24	)	)	PUNCT
ejpam-5611	45	25	∫	∫	PROPN
ejpam-5611	46	1	[	[	X
ejpam-5611	46	2	a	a	X
ejpam-5611	46	3	,	,	PUNCT
ejpam-5611	46	4	b	b	NOUN
ejpam-5611	46	5	]	]	X
ejpam-5611	46	6	f.	f.	PROPN
ejpam-5611	46	7	definition	definition	NOUN
ejpam-5611	46	8	3	3	NUM
ejpam-5611	46	9	.	.	PUNCT
ejpam-5611	47	1	[	[	X
ejpam-5611	47	2	6	6	NUM
ejpam-5611	47	3	]	]	PUNCT
ejpam-5611	47	4	let	let	VERB
ejpam-5611	47	5	g	g	NOUN
ejpam-5611	47	6	:	:	PUNCT
ejpam-5611	47	7	[	[	X
ejpam-5611	47	8	a	a	X
ejpam-5611	47	9	,	,	PUNCT
ejpam-5611	47	10	b	b	NOUN
ejpam-5611	47	11	]	]	X
ejpam-5611	47	12	→	→	PUNCT
ejpam-5611	47	13	r.	r.	X
ejpam-5611	47	14	the	the	DET
ejpam-5611	47	15	total	total	ADJ
ejpam-5611	47	16	variation	variation	NOUN
ejpam-5611	47	17	of	of	ADP
ejpam-5611	47	18	g	g	NOUN
ejpam-5611	47	19	over	over	ADP
ejpam-5611	47	20	[	[	X
ejpam-5611	47	21	a	a	DET
ejpam-5611	47	22	,	,	PUNCT
ejpam-5611	47	23	b	b	NOUN
ejpam-5611	47	24	]	]	PUNCT
ejpam-5611	47	25	is	be	AUX
ejpam-5611	47	26	given	give	VERB
ejpam-5611	47	27	by	by	ADP
ejpam-5611	47	28	v	v	NOUN
ejpam-5611	47	29	(	(	PUNCT
ejpam-5611	47	30	g	g	NOUN
ejpam-5611	47	31	;	;	PUNCT
ejpam-5611	47	32	[	[	X
ejpam-5611	47	33	a	a	X
ejpam-5611	47	34	,	,	PUNCT
ejpam-5611	47	35	b	b	NOUN
ejpam-5611	47	36	]	]	X
ejpam-5611	47	37	)	)	PUNCT
ejpam-5611	47	38	=	=	SYM
ejpam-5611	47	39	sup	sup	NOUN
ejpam-5611	47	40	{	{	PUNCT
ejpam-5611	47	41	∑	∑	PROPN
ejpam-5611	47	42	[	[	X
ejpam-5611	47	43	u	u	NOUN
ejpam-5611	47	44	,	,	PUNCT
ejpam-5611	47	45	v]∈d	v]∈d	ADJ
ejpam-5611	47	46	∣∣∆g([u	∣∣∆g([u	ADJ
ejpam-5611	47	47	,	,	PUNCT
ejpam-5611	47	48	v	v	NOUN
ejpam-5611	47	49	]	]	PUNCT
ejpam-5611	47	50	)	)	PUNCT
ejpam-5611	47	51	∣∣	∣∣	PUNCT
ejpam-5611	47	52	:	:	PUNCT
ejpam-5611	48	1	d	d	X
ejpam-5611	48	2	is	be	AUX
ejpam-5611	48	3	a	a	DET
ejpam-5611	48	4	division	division	NOUN
ejpam-5611	48	5	of	of	ADP
ejpam-5611	48	6	[	[	X
ejpam-5611	48	7	a	a	X
ejpam-5611	48	8	,	,	PUNCT
ejpam-5611	48	9	b	b	NOUN
ejpam-5611	48	10	]	]	X
ejpam-5611	48	11	}	}	PUNCT
ejpam-5611	48	12	,	,	PUNCT
ejpam-5611	48	13	where	where	SCONJ
ejpam-5611	48	14	∆g([u	∆g([u	NOUN
ejpam-5611	48	15	,	,	PUNCT
ejpam-5611	48	16	v	v	NOUN
ejpam-5611	48	17	]	]	X
ejpam-5611	48	18	)	)	PUNCT
ejpam-5611	48	19	=	=	SYM
ejpam-5611	48	20	∑	∑	PROPN
ejpam-5611	48	21	t∈v[u	t∈v[u	PROPN
ejpam-5611	48	22	,	,	PUNCT
ejpam-5611	48	23	v	v	NOUN
ejpam-5611	48	24	]	]	X
ejpam-5611	48	25	g(t	g(t	PROPN
ejpam-5611	48	26	)	)	PUNCT
ejpam-5611	48	27	n∏	n∏	PROPN
ejpam-5611	49	1	k=1	k=1	X
ejpam-5611	49	2	(	(	PUNCT
ejpam-5611	49	3	−1)χ{uk}(tk	−1)χ{uk}(tk	NOUN
ejpam-5611	49	4	)	)	PUNCT
ejpam-5611	49	5	,	,	PUNCT
ejpam-5611	49	6	t	t	PROPN
ejpam-5611	49	7	=	=	SYM
ejpam-5611	49	8	(	(	PUNCT
ejpam-5611	49	9	t1	t1	NOUN
ejpam-5611	49	10	,	,	PUNCT
ejpam-5611	49	11	t2	t2	NOUN
ejpam-5611	49	12	,	,	PUNCT
ejpam-5611	49	13	·	·	PUNCT
ejpam-5611	49	14	·	·	PUNCT
ejpam-5611	49	15	·	·	PUNCT
ejpam-5611	49	16	,	,	PUNCT
ejpam-5611	49	17	tn	tn	PROPN
ejpam-5611	49	18	)	)	PUNCT
ejpam-5611	49	19	and	and	CCONJ
ejpam-5611	49	20	v[u	v[u	PROPN
ejpam-5611	49	21	,	,	PUNCT
ejpam-5611	49	22	v	v	NOUN
ejpam-5611	49	23	]	]	X
ejpam-5611	49	24	is	be	AUX
ejpam-5611	49	25	the	the	DET
ejpam-5611	49	26	set	set	NOUN
ejpam-5611	49	27	of	of	ADP
ejpam-5611	49	28	vertices	vertex	NOUN
ejpam-5611	49	29	in	in	ADP
ejpam-5611	49	30	[	[	X
ejpam-5611	49	31	u	u	NOUN
ejpam-5611	49	32	,	,	PUNCT
ejpam-5611	49	33	v	v	NOUN
ejpam-5611	49	34	]	]	X
ejpam-5611	49	35	=	=	SYM
ejpam-5611	49	36	∏n	∏n	PROPN
ejpam-5611	49	37	k=1[uk	k=1[uk	PROPN
ejpam-5611	49	38	,	,	PUNCT
ejpam-5611	49	39	vk	vk	ADP
ejpam-5611	49	40	]	]	PUNCT
ejpam-5611	49	41	.	.	PUNCT
ejpam-5611	50	1	if	if	SCONJ
ejpam-5611	50	2	v	v	INTJ
ejpam-5611	50	3	(	(	PUNCT
ejpam-5611	50	4	g	g	NOUN
ejpam-5611	50	5	,	,	PUNCT
ejpam-5611	50	6	[	[	X
ejpam-5611	50	7	a	a	X
ejpam-5611	50	8	,	,	PUNCT
ejpam-5611	50	9	b	b	NOUN
ejpam-5611	50	10	]	]	X
ejpam-5611	50	11	)	)	PUNCT
ejpam-5611	50	12	<	<	X
ejpam-5611	51	1	+	+	PROPN
ejpam-5611	51	2	∞	∞	PROPN
ejpam-5611	51	3	,	,	PUNCT
ejpam-5611	51	4	then	then	ADV
ejpam-5611	51	5	g	g	PROPN
ejpam-5611	51	6	is	be	AUX
ejpam-5611	51	7	said	say	VERB
ejpam-5611	51	8	to	to	PART
ejpam-5611	51	9	be	be	AUX
ejpam-5611	51	10	a	a	DET
ejpam-5611	51	11	function	function	NOUN
ejpam-5611	51	12	of	of	ADP
ejpam-5611	51	13	bounded	bounded	ADJ
ejpam-5611	51	14	variation	variation	NOUN
ejpam-5611	51	15	on	on	ADP
ejpam-5611	51	16	[	[	X
ejpam-5611	51	17	a	a	X
ejpam-5611	51	18	,	,	PUNCT
ejpam-5611	51	19	b	b	NOUN
ejpam-5611	51	20	]	]	PUNCT
ejpam-5611	51	21	.	.	PUNCT
ejpam-5611	52	1	example	example	NOUN
ejpam-5611	53	1	1	1	NUM
ejpam-5611	53	2	.	.	PUNCT
ejpam-5611	53	3	(	(	PUNCT
ejpam-5611	53	4	i	i	NOUN
ejpam-5611	53	5	)	)	PUNCT
ejpam-5611	53	6	for	for	ADP
ejpam-5611	53	7	n	n	NOUN
ejpam-5611	53	8	=	=	SYM
ejpam-5611	53	9	2	2	NUM
ejpam-5611	53	10	,	,	PUNCT
ejpam-5611	53	11	we	we	PRON
ejpam-5611	53	12	have	have	VERB
ejpam-5611	53	13	∆g([u1	∆g([u1	VERB
ejpam-5611	53	14	,	,	PUNCT
ejpam-5611	53	15	v1])×	v1])×	X
ejpam-5611	54	1	[	[	X
ejpam-5611	54	2	u2	u2	NOUN
ejpam-5611	54	3	,	,	PUNCT
ejpam-5611	54	4	v2	v2	NOUN
ejpam-5611	54	5	]	]	X
ejpam-5611	54	6	=	=	SYM
ejpam-5611	54	7	g(v1	g(v1	NOUN
ejpam-5611	54	8	,	,	PUNCT
ejpam-5611	54	9	v2)−	v2)−	ADJ
ejpam-5611	54	10	g(u1	g(u1	NOUN
ejpam-5611	54	11	,	,	PUNCT
ejpam-5611	54	12	v2	v2	NOUN
ejpam-5611	54	13	)	)	PUNCT
ejpam-5611	54	14	+	+	CCONJ
ejpam-5611	54	15	g(u1	g(u1	ADJ
ejpam-5611	54	16	,	,	PUNCT
ejpam-5611	54	17	u2)−	u2)−	NOUN
ejpam-5611	54	18	g(v1	g(v1	NOUN
ejpam-5611	54	19	,	,	PUNCT
ejpam-5611	54	20	u2	u2	PROPN
ejpam-5611	54	21	)	)	PUNCT
ejpam-5611	54	22	;	;	PUNCT
ejpam-5611	54	23	(	(	PUNCT
ejpam-5611	54	24	ii	ii	NOUN
ejpam-5611	54	25	)	)	PUNCT
ejpam-5611	54	26	for	for	ADP
ejpam-5611	54	27	n	n	NOUN
ejpam-5611	54	28	=	=	SYM
ejpam-5611	54	29	1	1	NUM
ejpam-5611	54	30	,	,	PUNCT
ejpam-5611	54	31	we	we	PRON
ejpam-5611	54	32	have	have	VERB
ejpam-5611	54	33	∆g([u1	∆g([u1	VERB
ejpam-5611	54	34	,	,	PUNCT
ejpam-5611	54	35	v1	v1	NOUN
ejpam-5611	54	36	]	]	PUNCT
ejpam-5611	54	37	)	)	PUNCT
ejpam-5611	54	38	=	=	SYM
ejpam-5611	54	39	g(v1)−	g(v1)−	PROPN
ejpam-5611	54	40	g(u1	g(u1	NOUN
ejpam-5611	54	41	)	)	PUNCT
ejpam-5611	54	42	.	.	PUNCT
ejpam-5611	55	1	remark	remark	PROPN
ejpam-5611	55	2	1	1	NUM
ejpam-5611	55	3	.	.	PUNCT
ejpam-5611	56	1	the	the	DET
ejpam-5611	56	2	total	total	ADJ
ejpam-5611	56	3	variation	variation	NOUN
ejpam-5611	56	4	in	in	ADP
ejpam-5611	56	5	n	n	CCONJ
ejpam-5611	56	6	-	-	PUNCT
ejpam-5611	56	7	dimensional	dimensional	ADJ
ejpam-5611	56	8	euclidean	euclidean	ADJ
ejpam-5611	56	9	space	space	NOUN
ejpam-5611	56	10	is	be	AUX
ejpam-5611	56	11	an	an	DET
ejpam-5611	56	12	extension	extension	NOUN
ejpam-5611	56	13	of	of	ADP
ejpam-5611	56	14	the	the	DET
ejpam-5611	56	15	usual	usual	ADJ
ejpam-5611	56	16	total	total	ADJ
ejpam-5611	56	17	variation	variation	NOUN
ejpam-5611	56	18	in	in	ADP
ejpam-5611	56	19	euclidean	euclidean	ADJ
ejpam-5611	56	20	space	space	NOUN
ejpam-5611	56	21	.	.	PUNCT
ejpam-5611	57	1	definition	definition	NOUN
ejpam-5611	57	2	4	4	NUM
ejpam-5611	57	3	.	.	PUNCT
ejpam-5611	58	1	[	[	X
ejpam-5611	58	2	7	7	X
ejpam-5611	58	3	]	]	X
ejpam-5611	58	4	a	a	DET
ejpam-5611	58	5	topological	topological	ADJ
ejpam-5611	58	6	space	space	NOUN
ejpam-5611	58	7	is	be	AUX
ejpam-5611	58	8	second	second	ADV
ejpam-5611	58	9	countable	countable	ADJ
ejpam-5611	58	10	if	if	SCONJ
ejpam-5611	58	11	it	it	PRON
ejpam-5611	58	12	has	have	VERB
ejpam-5611	58	13	a	a	DET
ejpam-5611	58	14	countable	countable	ADJ
ejpam-5611	58	15	basis	basis	NOUN
ejpam-5611	58	16	.	.	PUNCT
ejpam-5611	59	1	definition	definition	NOUN
ejpam-5611	59	2	5	5	NUM
ejpam-5611	59	3	.	.	PUNCT
ejpam-5611	60	1	[	[	X
ejpam-5611	60	2	7	7	X
ejpam-5611	60	3	]	]	X
ejpam-5611	60	4	a	a	DET
ejpam-5611	60	5	topological	topological	ADJ
ejpam-5611	60	6	spacem	spacem	NOUN
ejpam-5611	60	7	is	be	AUX
ejpam-5611	60	8	locally	locally	ADV
ejpam-5611	60	9	euclidean	euclidean	ADJ
ejpam-5611	60	10	of	of	ADP
ejpam-5611	60	11	dimension	dimension	NOUN
ejpam-5611	60	12	n	n	CCONJ
ejpam-5611	60	13	if	if	SCONJ
ejpam-5611	60	14	every	every	DET
ejpam-5611	60	15	point	point	NOUN
ejpam-5611	60	16	p	p	NOUN
ejpam-5611	60	17	∈m	∈m	NOUN
ejpam-5611	60	18	has	have	VERB
ejpam-5611	60	19	a	a	DET
ejpam-5611	60	20	neighborhood	neighborhood	NOUN
ejpam-5611	60	21	up	up	ADP
ejpam-5611	60	22	such	such	ADJ
ejpam-5611	60	23	that	that	SCONJ
ejpam-5611	60	24	there	there	PRON
ejpam-5611	60	25	is	be	VERB
ejpam-5611	60	26	a	a	DET
ejpam-5611	60	27	homeomorphism	homeomorphism	NOUN
ejpam-5611	60	28	ϕ	ϕ	NOUN
ejpam-5611	60	29	from	from	ADP
ejpam-5611	60	30	up	up	ADP
ejpam-5611	60	31	onto	onto	ADP
ejpam-5611	60	32	an	an	DET
ejpam-5611	60	33	open	open	ADJ
ejpam-5611	60	34	subset	subset	ADJ
ejpam-5611	60	35	op	op	NOUN
ejpam-5611	60	36	of	of	ADP
ejpam-5611	60	37	rn	rn	PROPN
ejpam-5611	60	38	.	.	PUNCT
ejpam-5611	61	1	we	we	PRON
ejpam-5611	61	2	call	call	VERB
ejpam-5611	61	3	the	the	DET
ejpam-5611	61	4	pair	pair	NOUN
ejpam-5611	61	5	(	(	PUNCT
ejpam-5611	61	6	u	u	NOUN
ejpam-5611	61	7	,	,	PUNCT
ejpam-5611	61	8	ϕ	ϕ	X
ejpam-5611	61	9	:	:	PUNCT
ejpam-5611	61	10	u	u	PROPN
ejpam-5611	61	11	→	→	SYM
ejpam-5611	61	12	rn	rn	PROPN
ejpam-5611	61	13	)	)	PUNCT
ejpam-5611	61	14	a	a	DET
ejpam-5611	61	15	chart	chart	NOUN
ejpam-5611	61	16	,	,	PUNCT
ejpam-5611	61	17	u	u	NOUN
ejpam-5611	61	18	a	a	DET
ejpam-5611	61	19	coordinate	coordinate	ADJ
ejpam-5611	61	20	neighborhood	neighborhood	NOUN
ejpam-5611	61	21	or	or	CCONJ
ejpam-5611	61	22	a	a	DET
ejpam-5611	61	23	coordinate	coordinate	NOUN
ejpam-5611	61	24	open	open	ADJ
ejpam-5611	61	25	set	set	NOUN
ejpam-5611	61	26	,	,	PUNCT
ejpam-5611	61	27	and	and	CCONJ
ejpam-5611	61	28	ϕ	ϕ	X
ejpam-5611	61	29	a	a	DET
ejpam-5611	61	30	coordinate	coordinate	NOUN
ejpam-5611	61	31	map	map	NOUN
ejpam-5611	61	32	or	or	CCONJ
ejpam-5611	61	33	coordinate	coordinate	VERB
ejpam-5611	61	34	system	system	NOUN
ejpam-5611	61	35	on	on	ADP
ejpam-5611	61	36	u	u	NOUN
ejpam-5611	61	37	.	.	PUNCT
ejpam-5611	62	1	we	we	PRON
ejpam-5611	62	2	say	say	VERB
ejpam-5611	62	3	that	that	SCONJ
ejpam-5611	62	4	a	a	DET
ejpam-5611	62	5	chart	chart	NOUN
ejpam-5611	62	6	(	(	PUNCT
ejpam-5611	62	7	u	u	NOUN
ejpam-5611	62	8	,	,	PUNCT
ejpam-5611	62	9	ϕ	ϕ	NOUN
ejpam-5611	62	10	)	)	PUNCT
ejpam-5611	62	11	is	be	AUX
ejpam-5611	62	12	centered	center	VERB
ejpam-5611	62	13	at	at	ADP
ejpam-5611	62	14	p	p	PROPN
ejpam-5611	62	15	∈	∈	PROPN
ejpam-5611	62	16	u	u	NOUN
ejpam-5611	62	17	if	if	SCONJ
ejpam-5611	62	18	ϕ(p	ϕ(p	X
ejpam-5611	62	19	)	)	PUNCT
ejpam-5611	62	20	=	=	NOUN
ejpam-5611	63	1	0	0	X
ejpam-5611	63	2	.	.	PUNCT
ejpam-5611	64	1	a	a	DET
ejpam-5611	64	2	chart	chart	NOUN
ejpam-5611	64	3	(	(	PUNCT
ejpam-5611	64	4	u	u	NOUN
ejpam-5611	64	5	,	,	PUNCT
ejpam-5611	64	6	ϕ	ϕ	NOUN
ejpam-5611	64	7	)	)	PUNCT
ejpam-5611	64	8	about	about	ADP
ejpam-5611	64	9	p	p	PRON
ejpam-5611	64	10	simply	simply	ADV
ejpam-5611	64	11	means	mean	VERB
ejpam-5611	64	12	that	that	SCONJ
ejpam-5611	64	13	(	(	PUNCT
ejpam-5611	64	14	u	u	NOUN
ejpam-5611	64	15	,	,	PUNCT
ejpam-5611	64	16	ϕ	ϕ	NOUN
ejpam-5611	64	17	)	)	PUNCT
ejpam-5611	64	18	is	be	AUX
ejpam-5611	64	19	a	a	DET
ejpam-5611	64	20	chart	chart	NOUN
ejpam-5611	64	21	and	and	CCONJ
ejpam-5611	64	22	p	p	NOUN
ejpam-5611	64	23	∈	∈	PROPN
ejpam-5611	64	24	u	u	NOUN
ejpam-5611	64	25	.	.	PUNCT
ejpam-5611	65	1	definition	definition	NOUN
ejpam-5611	65	2	6	6	NUM
ejpam-5611	65	3	.	.	PUNCT
ejpam-5611	66	1	[	[	X
ejpam-5611	66	2	7	7	X
ejpam-5611	66	3	]	]	X
ejpam-5611	66	4	a	a	DET
ejpam-5611	66	5	topological	topological	ADJ
ejpam-5611	66	6	manifold	manifold	NOUN
ejpam-5611	66	7	of	of	ADP
ejpam-5611	66	8	dimension	dimension	NOUN
ejpam-5611	66	9	n	n	PRON
ejpam-5611	66	10	is	be	AUX
ejpam-5611	66	11	a	a	DET
ejpam-5611	66	12	hausdorff	hausdorff	NOUN
ejpam-5611	66	13	,	,	PUNCT
ejpam-5611	66	14	second	second	ADV
ejpam-5611	66	15	countable	countable	ADJ
ejpam-5611	66	16	,	,	PUNCT
ejpam-5611	66	17	locally	locally	ADV
ejpam-5611	66	18	euclidean	euclidean	ADJ
ejpam-5611	66	19	space	space	NOUN
ejpam-5611	66	20	of	of	ADP
ejpam-5611	66	21	dimension	dimension	NOUN
ejpam-5611	66	22	n.	n.	PROPN
ejpam-5611	66	23	example	example	NOUN
ejpam-5611	67	1	2	2	NUM
ejpam-5611	67	2	.	.	PUNCT
ejpam-5611	68	1	[	[	X
ejpam-5611	68	2	7	7	X
ejpam-5611	68	3	]	]	X
ejpam-5611	68	4	the	the	DET
ejpam-5611	68	5	euclidean	euclidean	ADJ
ejpam-5611	68	6	space	space	NOUN
ejpam-5611	68	7	rn	rn	PROPN
ejpam-5611	68	8	is	be	AUX
ejpam-5611	68	9	covered	cover	VERB
ejpam-5611	68	10	by	by	ADP
ejpam-5611	68	11	a	a	DET
ejpam-5611	68	12	single	single	ADJ
ejpam-5611	68	13	chart	chart	NOUN
ejpam-5611	68	14	(	(	PUNCT
ejpam-5611	68	15	rn	rn	PROPN
ejpam-5611	68	16	,	,	PUNCT
ejpam-5611	68	17	1rn	1rn	ADJ
ejpam-5611	68	18	)	)	PUNCT
ejpam-5611	68	19	,	,	PUNCT
ejpam-5611	68	20	where	where	SCONJ
ejpam-5611	68	21	1rn	1rn	ADJ
ejpam-5611	68	22	:	:	PUNCT
ejpam-5611	68	23	rn	rn	PROPN
ejpam-5611	68	24	→	→	PROPN
ejpam-5611	68	25	rn	rn	PROPN
ejpam-5611	68	26	is	be	AUX
ejpam-5611	68	27	the	the	DET
ejpam-5611	68	28	identity	identity	NOUN
ejpam-5611	68	29	map	map	NOUN
ejpam-5611	68	30	.	.	PUNCT
ejpam-5611	69	1	it	it	PRON
ejpam-5611	69	2	is	be	AUX
ejpam-5611	69	3	a	a	DET
ejpam-5611	69	4	prime	prime	ADJ
ejpam-5611	69	5	example	example	NOUN
ejpam-5611	69	6	of	of	ADP
ejpam-5611	69	7	a	a	DET
ejpam-5611	69	8	topological	topological	ADJ
ejpam-5611	69	9	manifold	manifold	NOUN
ejpam-5611	69	10	.	.	PUNCT
ejpam-5611	70	1	every	every	DET
ejpam-5611	70	2	open	open	ADJ
ejpam-5611	70	3	subset	subset	ADJ
ejpam-5611	70	4	u	u	NOUN
ejpam-5611	70	5	of	of	ADP
ejpam-5611	70	6	rn	rn	PROPN
ejpam-5611	70	7	is	be	AUX
ejpam-5611	70	8	also	also	ADV
ejpam-5611	70	9	a	a	DET
ejpam-5611	70	10	topological	topological	ADJ
ejpam-5611	70	11	manifold	manifold	NOUN
ejpam-5611	70	12	,	,	PUNCT
ejpam-5611	70	13	with	with	ADP
ejpam-5611	70	14	chart	chart	NOUN
ejpam-5611	70	15	(	(	PUNCT
ejpam-5611	70	16	u	u	NOUN
ejpam-5611	70	17	,	,	PUNCT
ejpam-5611	70	18	1rn	1rn	NUM
ejpam-5611	70	19	)	)	PUNCT
ejpam-5611	70	20	.	.	PUNCT
ejpam-5611	71	1	g.	g.	PROPN
ejpam-5611	71	2	flores	flores	PROPN
ejpam-5611	71	3	,	,	PUNCT
ejpam-5611	71	4	a.	a.	PROPN
ejpam-5611	71	5	flores	flores	PROPN
ejpam-5611	71	6	/	/	SYM
ejpam-5611	71	7	eur	eur	PROPN
ejpam-5611	71	8	.	.	PUNCT
ejpam-5611	72	1	j.	j.	PROPN
ejpam-5611	72	2	pure	pure	PROPN
ejpam-5611	72	3	appl	appl	PROPN
ejpam-5611	72	4	.	.	PROPN
ejpam-5611	72	5	math	math	PROPN
ejpam-5611	72	6	,	,	PUNCT
ejpam-5611	72	7	18	18	NUM
ejpam-5611	72	8	(	(	PUNCT
ejpam-5611	72	9	2	2	NUM
ejpam-5611	72	10	)	)	PUNCT
ejpam-5611	72	11	(	(	PUNCT
ejpam-5611	72	12	2025	2025	NUM
ejpam-5611	72	13	)	)	PUNCT
ejpam-5611	72	14	,	,	PUNCT
ejpam-5611	72	15	5611	5611	NUM
ejpam-5611	72	16	4	4	NUM
ejpam-5611	72	17	of	of	ADP
ejpam-5611	72	18	16	16	NUM
ejpam-5611	72	19	3	3	NUM
ejpam-5611	72	20	.	.	PUNCT
ejpam-5611	72	21	main	main	ADJ
ejpam-5611	72	22	results	result	NOUN
ejpam-5611	72	23	lemma	lemma	PROPN
ejpam-5611	72	24	1	1	X
ejpam-5611	72	25	.	.	PUNCT
ejpam-5611	73	1	let	let	VERB
ejpam-5611	73	2	u	u	PRON
ejpam-5611	73	3	be	be	AUX
ejpam-5611	73	4	an	an	DET
ejpam-5611	73	5	open	open	ADJ
ejpam-5611	73	6	subset	subset	NOUN
ejpam-5611	73	7	of	of	ADP
ejpam-5611	73	8	a	a	DET
ejpam-5611	73	9	compact	compact	ADJ
ejpam-5611	73	10	interval	interval	NOUN
ejpam-5611	73	11	e∗	e∗	PROPN
ejpam-5611	73	12	in	in	ADP
ejpam-5611	73	13	rr	rr	PROPN
ejpam-5611	73	14	and	and	CCONJ
ejpam-5611	73	15	ψ	ψ	X
ejpam-5611	73	16	:	:	PUNCT
ejpam-5611	73	17	u	u	X
ejpam-5611	73	18	→	→	PUNCT
ejpam-5611	73	19	ψ(u	ψ(u	PROPN
ejpam-5611	73	20	)	)	PUNCT
ejpam-5611	73	21	be	be	VERB
ejpam-5611	73	22	c1	c1	NOUN
ejpam-5611	73	23	-	-	PUNCT
ejpam-5611	73	24	diffeomorphism	diffeomorphism	NOUN
ejpam-5611	73	25	which	which	PRON
ejpam-5611	73	26	is	be	AUX
ejpam-5611	73	27	monotone	monotone	ADJ
ejpam-5611	73	28	.	.	PUNCT
ejpam-5611	74	1	suppose	suppose	VERB
ejpam-5611	74	2	that	that	SCONJ
ejpam-5611	74	3	e	e	PROPN
ejpam-5611	74	4	is	be	AUX
ejpam-5611	74	5	a	a	DET
ejpam-5611	74	6	compact	compact	ADJ
ejpam-5611	74	7	interval	interval	NOUN
ejpam-5611	74	8	such	such	ADJ
ejpam-5611	74	9	that	that	SCONJ
ejpam-5611	74	10	e	e	PROPN
ejpam-5611	74	11	⊆	⊆	NUM
ejpam-5611	74	12	ψ(u	ψ(u	PROPN
ejpam-5611	74	13	)	)	PUNCT
ejpam-5611	74	14	⊆	⊆	NUM
ejpam-5611	74	15	rn	rn	PROPN
ejpam-5611	74	16	and	and	CCONJ
ejpam-5611	74	17	φ	φ	NUM
ejpam-5611	74	18	:	:	PUNCT
ejpam-5611	74	19	e	e	X
ejpam-5611	74	20	→	→	SYM
ejpam-5611	74	21	r	r	NOUN
ejpam-5611	74	22	is	be	AUX
ejpam-5611	74	23	continuous	continuous	ADJ
ejpam-5611	74	24	and	and	CCONJ
ejpam-5611	74	25	g	g	NOUN
ejpam-5611	74	26	:	:	PUNCT
ejpam-5611	74	27	e	e	X
ejpam-5611	74	28	→	→	SYM
ejpam-5611	74	29	r	r	NOUN
ejpam-5611	74	30	be	be	AUX
ejpam-5611	74	31	a	a	DET
ejpam-5611	74	32	function	function	NOUN
ejpam-5611	74	33	of	of	ADP
ejpam-5611	74	34	bounded	bounded	ADJ
ejpam-5611	74	35	variation	variation	NOUN
ejpam-5611	74	36	.	.	PUNCT
ejpam-5611	75	1	then	then	ADV
ejpam-5611	75	2	(	(	PUNCT
ejpam-5611	75	3	r	r	NOUN
ejpam-5611	75	4	)	)	PUNCT
ejpam-5611	75	5	∫	∫	NOUN
ejpam-5611	75	6	e	e	PROPN
ejpam-5611	75	7	φ	φ	PROPN
ejpam-5611	75	8	dg	dg	PROPN
ejpam-5611	76	1	=	=	SYM
ejpam-5611	76	2	(	(	PUNCT
ejpam-5611	76	3	r	r	NOUN
ejpam-5611	76	4	)	)	PUNCT
ejpam-5611	76	5	∫	∫	PROPN
ejpam-5611	76	6	ψ−1(e	ψ−1(e	PROPN
ejpam-5611	76	7	)	)	PUNCT
ejpam-5611	76	8	(	(	PUNCT
ejpam-5611	76	9	φ	φ	NUM
ejpam-5611	76	10	◦	◦	VERB
ejpam-5611	76	11	ψ)|detψ|	ψ)|detψ|	PROPN
ejpam-5611	76	12	dg	dg	PROPN
ejpam-5611	76	13	,	,	PUNCT
ejpam-5611	76	14	where	where	SCONJ
ejpam-5611	76	15	(	(	PUNCT
ejpam-5611	76	16	r	r	NOUN
ejpam-5611	76	17	)	)	PUNCT
ejpam-5611	76	18	∫	∫	NOUN
ejpam-5611	77	1	e	e	PROPN
ejpam-5611	77	2	φ	φ	PROPN
ejpam-5611	77	3	dg	dg	PROPN
ejpam-5611	77	4	is	be	AUX
ejpam-5611	77	5	the	the	DET
ejpam-5611	77	6	riemann	riemann	PROPN
ejpam-5611	77	7	-	-	PUNCT
ejpam-5611	77	8	stieltjes	stieltjes	NOUN
ejpam-5611	77	9	integral	integral	ADJ
ejpam-5611	77	10	of	of	ADP
ejpam-5611	77	11	φ	φ	PROPN
ejpam-5611	77	12	with	with	ADP
ejpam-5611	77	13	respect	respect	NOUN
ejpam-5611	77	14	to	to	ADP
ejpam-5611	77	15	g	g	NOUN
ejpam-5611	77	16	on	on	ADP
ejpam-5611	77	17	e	e	PROPN
ejpam-5611	77	18	and	and	CCONJ
ejpam-5611	77	19	|detψ|	|detψ|	PROPN
ejpam-5611	77	20	is	be	AUX
ejpam-5611	77	21	the	the	DET
ejpam-5611	77	22	euclidean	euclidean	ADJ
ejpam-5611	77	23	norm	norm	NOUN
ejpam-5611	77	24	of	of	ADP
ejpam-5611	77	25	the	the	DET
ejpam-5611	77	26	partial	partial	ADJ
ejpam-5611	77	27	derivatives	derivative	NOUN
ejpam-5611	77	28	of	of	ADP
ejpam-5611	77	29	ψ	ψ	NOUN
ejpam-5611	77	30	.	.	PUNCT
ejpam-5611	78	1	proof	proof	NOUN
ejpam-5611	78	2	:	:	PUNCT
ejpam-5611	78	3	since	since	SCONJ
ejpam-5611	78	4	φ	φ	PROPN
ejpam-5611	78	5	is	be	AUX
ejpam-5611	78	6	continuous	continuous	ADJ
ejpam-5611	78	7	and	and	CCONJ
ejpam-5611	78	8	g	g	NOUN
ejpam-5611	78	9	is	be	AUX
ejpam-5611	78	10	of	of	ADP
ejpam-5611	78	11	bounded	bounded	ADJ
ejpam-5611	78	12	variation	variation	NOUN
ejpam-5611	78	13	,	,	PUNCT
ejpam-5611	78	14	then	then	ADV
ejpam-5611	78	15	(	(	PUNCT
ejpam-5611	78	16	r	r	NOUN
ejpam-5611	78	17	)	)	PUNCT
ejpam-5611	78	18	∫	∫	NOUN
ejpam-5611	78	19	e	e	PROPN
ejpam-5611	78	20	φ	φ	PROPN
ejpam-5611	78	21	dg	dg	PROPN
ejpam-5611	78	22	exists	exist	VERB
ejpam-5611	78	23	in	in	ADP
ejpam-5611	78	24	r.	r.	PROPN
ejpam-5611	78	25	thus	thus	ADV
ejpam-5611	78	26	,	,	PUNCT
ejpam-5611	78	27	for	for	ADP
ejpam-5611	78	28	each	each	PRON
ejpam-5611	78	29	ϵ	ϵ	X
ejpam-5611	78	30	>	>	X
ejpam-5611	78	31	0	0	NUM
ejpam-5611	78	32	,	,	PUNCT
ejpam-5611	78	33	there	there	PRON
ejpam-5611	78	34	exists	exist	VERB
ejpam-5611	78	35	a	a	DET
ejpam-5611	78	36	constant	constant	ADJ
ejpam-5611	78	37	δ1	δ1	NOUN
ejpam-5611	78	38	>	>	X
ejpam-5611	78	39	0	0	NUM
ejpam-5611	78	40	such	such	ADJ
ejpam-5611	78	41	that	that	PRON
ejpam-5611	78	42	for	for	ADP
ejpam-5611	78	43	any	any	DET
ejpam-5611	78	44	δ1	δ1	NOUN
ejpam-5611	78	45	-	-	PUNCT
ejpam-5611	78	46	fine	fine	NOUN
ejpam-5611	78	47	division	division	NOUN
ejpam-5611	78	48	d	d	NOUN
ejpam-5611	78	49	=	=	PRON
ejpam-5611	78	50	{	{	PUNCT
ejpam-5611	78	51	(	(	PUNCT
ejpam-5611	78	52	ξ	ξ	PROPN
ejpam-5611	78	53	,	,	PUNCT
ejpam-5611	78	54	i	i	NOUN
ejpam-5611	78	55	)	)	PUNCT
ejpam-5611	78	56	}	}	PUNCT
ejpam-5611	78	57	of	of	ADP
ejpam-5611	78	58	e	e	NOUN
ejpam-5611	78	59	,	,	PUNCT
ejpam-5611	78	60	we	we	PRON
ejpam-5611	78	61	have∣∣∣∣∑	have∣∣∣∣∑	PROPN
ejpam-5611	78	62	d	d	X
ejpam-5611	78	63	φ(ξ)∆g(i)−	φ(ξ)∆g(i)−	PROPN
ejpam-5611	78	64	(	(	PUNCT
ejpam-5611	78	65	r	r	NOUN
ejpam-5611	78	66	)	)	PUNCT
ejpam-5611	78	67	∫	∫	NOUN
ejpam-5611	78	68	e	e	PROPN
ejpam-5611	78	69	φ	φ	PROPN
ejpam-5611	78	70	dg	dg	PROPN
ejpam-5611	78	71	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5611	78	72	<	<	X
ejpam-5611	78	73	ϵ	ϵ	X
ejpam-5611	78	74	2	2	NUM
ejpam-5611	78	75	.	.	PUNCT
ejpam-5611	79	1	(	(	PUNCT
ejpam-5611	79	2	3.1	3.1	NUM
ejpam-5611	79	3	)	)	PUNCT
ejpam-5611	79	4	note	note	NOUN
ejpam-5611	79	5	that	that	SCONJ
ejpam-5611	79	6	,	,	PUNCT
ejpam-5611	79	7	(	(	PUNCT
ejpam-5611	79	8	φ	φ	X
ejpam-5611	79	9	◦	◦	NOUN
ejpam-5611	79	10	ψ)|detψ|	ψ)|detψ|	NOUN
ejpam-5611	79	11	is	be	AUX
ejpam-5611	79	12	continuous	continuous	ADJ
ejpam-5611	79	13	on	on	ADP
ejpam-5611	79	14	ψ−1(e	ψ−1(e	PROPN
ejpam-5611	79	15	)	)	PUNCT
ejpam-5611	79	16	.	.	PUNCT
ejpam-5611	80	1	also	also	ADV
ejpam-5611	80	2	,	,	PUNCT
ejpam-5611	80	3	since	since	SCONJ
ejpam-5611	80	4	g	g	PROPN
ejpam-5611	80	5	is	be	AUX
ejpam-5611	80	6	a	a	DET
ejpam-5611	80	7	function	function	NOUN
ejpam-5611	80	8	of	of	ADP
ejpam-5611	80	9	bounded	bounded	ADJ
ejpam-5611	80	10	variation	variation	NOUN
ejpam-5611	80	11	on	on	ADP
ejpam-5611	80	12	ψ−1(e	ψ−1(e	PROPN
ejpam-5611	80	13	)	)	PUNCT
ejpam-5611	80	14	,	,	PUNCT
ejpam-5611	80	15	it	it	PRON
ejpam-5611	80	16	follows	follow	VERB
ejpam-5611	80	17	that	that	SCONJ
ejpam-5611	80	18	(	(	PUNCT
ejpam-5611	80	19	r	r	NOUN
ejpam-5611	80	20	)	)	PUNCT
ejpam-5611	80	21	∫	∫	PROPN
ejpam-5611	80	22	ψ−1(e	ψ−1(e	PROPN
ejpam-5611	80	23	)	)	PUNCT
ejpam-5611	80	24	(	(	PUNCT
ejpam-5611	80	25	φ	φ	NUM
ejpam-5611	80	26	◦	◦	NOUN
ejpam-5611	80	27	ψ)|detψ|	ψ)|detψ|	ADJ
ejpam-5611	80	28	dg	dg	NOUN
ejpam-5611	80	29	exists	exist	VERB
ejpam-5611	80	30	in	in	ADP
ejpam-5611	80	31	r	r	NOUN
ejpam-5611	80	32	;	;	PUNCT
ejpam-5611	80	33	hence	hence	ADV
ejpam-5611	80	34	there	there	PRON
ejpam-5611	80	35	exists	exist	VERB
ejpam-5611	80	36	a	a	DET
ejpam-5611	80	37	constant	constant	ADJ
ejpam-5611	80	38	δ0	δ0	NOUN
ejpam-5611	80	39	≤	≤	NOUN
ejpam-5611	80	40	δ1	δ1	NOUN
ejpam-5611	80	41	such	such	ADJ
ejpam-5611	80	42	that	that	PRON
ejpam-5611	80	43	for	for	ADP
ejpam-5611	80	44	any	any	DET
ejpam-5611	80	45	δ0	δ0	NOUN
ejpam-5611	80	46	-	-	PUNCT
ejpam-5611	80	47	fine	fine	ADJ
ejpam-5611	80	48	division	division	NOUN
ejpam-5611	80	49	d′	d′	X
ejpam-5611	80	50	=	=	SYM
ejpam-5611	80	51	{	{	PUNCT
ejpam-5611	80	52	(	(	PUNCT
ejpam-5611	80	53	t	t	PROPN
ejpam-5611	80	54	,	,	PUNCT
ejpam-5611	80	55	k	k	NOUN
ejpam-5611	80	56	)	)	PUNCT
ejpam-5611	80	57	}	}	PUNCT
ejpam-5611	80	58	of	of	ADP
ejpam-5611	80	59	ψ−1(e	ψ−1(e	PROPN
ejpam-5611	80	60	)	)	PUNCT
ejpam-5611	80	61	,	,	PUNCT
ejpam-5611	80	62	we	we	PRON
ejpam-5611	80	63	have∣∣∣∣∑	have∣∣∣∣∑	VERB
ejpam-5611	80	64	d′	d′	PROPN
ejpam-5611	80	65	(	(	PUNCT
ejpam-5611	80	66	φ	φ	PROPN
ejpam-5611	80	67	◦	◦	PROPN
ejpam-5611	80	68	ψ)(t)∆(g	ψ)(t)∆(g	PROPN
ejpam-5611	80	69	◦	◦	NOUN
ejpam-5611	80	70	ψ)(k)−	ψ)(k)−	ADJ
ejpam-5611	80	71	(	(	PUNCT
ejpam-5611	80	72	r	r	NOUN
ejpam-5611	80	73	)	)	PUNCT
ejpam-5611	80	74	∫	∫	PROPN
ejpam-5611	80	75	ψ−1(e	ψ−1(e	PROPN
ejpam-5611	80	76	)	)	PUNCT
ejpam-5611	81	1	(	(	PUNCT
ejpam-5611	81	2	φ	φ	NUM
ejpam-5611	81	3	◦	◦	NOUN
ejpam-5611	81	4	ψ)|detψ|	ψ)|detψ|	NOUN
ejpam-5611	81	5	dg	dg	VERB
ejpam-5611	81	6	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5611	81	7	<	<	X
ejpam-5611	81	8	ϵ	ϵ	X
ejpam-5611	81	9	2	2	NUM
ejpam-5611	81	10	.	.	PUNCT
ejpam-5611	82	1	(	(	PUNCT
ejpam-5611	82	2	3.2	3.2	NUM
ejpam-5611	82	3	)	)	PUNCT
ejpam-5611	82	4	since	since	SCONJ
ejpam-5611	82	5	ψ	ψ	NOUN
ejpam-5611	82	6	is	be	AUX
ejpam-5611	82	7	a	a	DET
ejpam-5611	82	8	diffeomorphism	diffeomorphism	NOUN
ejpam-5611	82	9	on	on	ADP
ejpam-5611	82	10	u	u	PROPN
ejpam-5611	82	11	,	,	PUNCT
ejpam-5611	82	12	ψ	ψ	X
ejpam-5611	82	13	is	be	AUX
ejpam-5611	82	14	continuous	continuous	ADJ
ejpam-5611	82	15	at	at	ADP
ejpam-5611	82	16	every	every	DET
ejpam-5611	82	17	point	point	NOUN
ejpam-5611	82	18	in	in	ADP
ejpam-5611	82	19	u	u	NOUN
ejpam-5611	82	20	.	.	PUNCT
ejpam-5611	83	1	since	since	SCONJ
ejpam-5611	83	2	e	e	PROPN
ejpam-5611	83	3	⊆	⊆	NUM
ejpam-5611	83	4	ψ(u	ψ(u	PROPN
ejpam-5611	83	5	)	)	PUNCT
ejpam-5611	83	6	,	,	PUNCT
ejpam-5611	83	7	we	we	PRON
ejpam-5611	83	8	have	have	VERB
ejpam-5611	83	9	ψ−1(e	ψ−1(e	PROPN
ejpam-5611	83	10	)	)	PUNCT
ejpam-5611	84	1	⊆	⊆	NUM
ejpam-5611	84	2	u	u	NOUN
ejpam-5611	84	3	.	.	PUNCT
ejpam-5611	85	1	hence	hence	ADV
ejpam-5611	85	2	,	,	PUNCT
ejpam-5611	85	3	ψ	ψ	PROPN
ejpam-5611	85	4	is	be	AUX
ejpam-5611	85	5	continuous	continuous	ADJ
ejpam-5611	85	6	at	at	ADP
ejpam-5611	85	7	every	every	DET
ejpam-5611	85	8	point	point	NOUN
ejpam-5611	85	9	in	in	ADP
ejpam-5611	85	10	ψ−1(e	ψ−1(e	PROPN
ejpam-5611	85	11	)	)	PUNCT
ejpam-5611	85	12	.	.	PUNCT
ejpam-5611	86	1	thus	thus	ADV
ejpam-5611	86	2	,	,	PUNCT
ejpam-5611	86	3	for	for	ADP
ejpam-5611	86	4	each	each	DET
ejpam-5611	86	5	x	x	SYM
ejpam-5611	86	6	∈	∈	PROPN
ejpam-5611	86	7	ψ−1(e	ψ−1(e	PROPN
ejpam-5611	86	8	)	)	PUNCT
ejpam-5611	86	9	and	and	CCONJ
ejpam-5611	86	10	δ1	δ1	VERB
ejpam-5611	86	11	>	>	X
ejpam-5611	86	12	0	0	PUNCT
ejpam-5611	86	13	there	there	PRON
ejpam-5611	86	14	exists	exist	VERB
ejpam-5611	86	15	δ2(x	δ2(x	X
ejpam-5611	86	16	)	)	PUNCT
ejpam-5611	86	17	>	>	X
ejpam-5611	86	18	0	0	NUM
ejpam-5611	86	19	such	such	ADJ
ejpam-5611	86	20	that	that	PRON
ejpam-5611	86	21	for	for	ADP
ejpam-5611	86	22	any	any	DET
ejpam-5611	86	23	y	y	PROPN
ejpam-5611	86	24	∈	∈	PROPN
ejpam-5611	86	25	b(x	b(x	NOUN
ejpam-5611	86	26	,	,	PUNCT
ejpam-5611	86	27	δ2(x	δ2(x	NOUN
ejpam-5611	86	28	)	)	PUNCT
ejpam-5611	86	29	)	)	PUNCT
ejpam-5611	86	30	,	,	PUNCT
ejpam-5611	86	31	|ψ(y)−	|ψ(y)−	NUM
ejpam-5611	86	32	ψ(x)|	ψ(x)|	PROPN
ejpam-5611	86	33	<	<	X
ejpam-5611	86	34	δ1	δ1	NOUN
ejpam-5611	86	35	.	.	PUNCT
ejpam-5611	87	1	for	for	ADP
ejpam-5611	87	2	each	each	DET
ejpam-5611	87	3	x	x	SYM
ejpam-5611	87	4	∈	∈	PROPN
ejpam-5611	87	5	ψ−1(e	ψ−1(e	PROPN
ejpam-5611	87	6	)	)	PUNCT
ejpam-5611	87	7	,	,	PUNCT
ejpam-5611	87	8	let	let	VERB
ejpam-5611	87	9	δ(x	δ(x	NOUN
ejpam-5611	87	10	)	)	PUNCT
ejpam-5611	87	11	=	=	SYM
ejpam-5611	87	12	min{δ0(x	min{δ0(x	NOUN
ejpam-5611	87	13	)	)	PUNCT
ejpam-5611	87	14	,	,	PUNCT
ejpam-5611	87	15	δ2(x	δ2(x	NOUN
ejpam-5611	87	16	)	)	PUNCT
ejpam-5611	87	17	}	}	PUNCT
ejpam-5611	87	18	.	.	PUNCT
ejpam-5611	88	1	now	now	ADV
ejpam-5611	88	2	,	,	PUNCT
ejpam-5611	88	3	let	let	VERB
ejpam-5611	88	4	d0	d0	NOUN
ejpam-5611	88	5	=	=	SYM
ejpam-5611	88	6	{	{	PUNCT
ejpam-5611	88	7	(	(	PUNCT
ejpam-5611	88	8	η	η	PROPN
ejpam-5611	88	9	,	,	PUNCT
ejpam-5611	88	10	j	j	NOUN
ejpam-5611	88	11	)	)	PUNCT
ejpam-5611	88	12	}	}	PUNCT
ejpam-5611	88	13	be	be	AUX
ejpam-5611	88	14	a	a	DET
ejpam-5611	88	15	fix	fix	NOUN
ejpam-5611	88	16	δ	δ	NOUN
ejpam-5611	88	17	-	-	PUNCT
ejpam-5611	88	18	fine	fine	ADJ
ejpam-5611	88	19	division	division	NOUN
ejpam-5611	88	20	of	of	ADP
ejpam-5611	88	21	ψ−1(e	ψ−1(e	PROPN
ejpam-5611	88	22	)	)	PUNCT
ejpam-5611	88	23	.	.	PUNCT
ejpam-5611	89	1	hence	hence	ADV
ejpam-5611	89	2	,	,	PUNCT
ejpam-5611	89	3	for	for	ADP
ejpam-5611	89	4	each	each	PRON
ejpam-5611	89	5	(	(	PUNCT
ejpam-5611	89	6	η	η	PROPN
ejpam-5611	89	7	,	,	PUNCT
ejpam-5611	89	8	j	j	NOUN
ejpam-5611	89	9	)	)	PUNCT
ejpam-5611	89	10	in	in	ADP
ejpam-5611	89	11	d0	d0	NOUN
ejpam-5611	89	12	and	and	CCONJ
ejpam-5611	89	13	x	x	SYM
ejpam-5611	89	14	∈	∈	PROPN
ejpam-5611	89	15	j	j	NOUN
ejpam-5611	89	16	we	we	PRON
ejpam-5611	89	17	have	have	VERB
ejpam-5611	89	18	|ψ(η)−	|ψ(η)−	NOUN
ejpam-5611	89	19	ψ(x)|	ψ(x)|	NOUN
ejpam-5611	89	20	<	<	X
ejpam-5611	89	21	δ1	δ1	NOUN
ejpam-5611	89	22	.	.	PUNCT
ejpam-5611	90	1	(	(	PUNCT
ejpam-5611	90	2	3.3	3.3	NUM
ejpam-5611	90	3	)	)	PUNCT
ejpam-5611	90	4	also	also	ADV
ejpam-5611	90	5	,	,	PUNCT
ejpam-5611	90	6	ψ(j	ψ(j	PROPN
ejpam-5611	90	7	)	)	PUNCT
ejpam-5611	90	8	is	be	AUX
ejpam-5611	90	9	a	a	DET
ejpam-5611	90	10	compact	compact	ADJ
ejpam-5611	90	11	interval	interval	NOUN
ejpam-5611	90	12	in	in	ADP
ejpam-5611	90	13	rn	rn	PROPN
ejpam-5611	90	14	that	that	PRON
ejpam-5611	90	15	partitions	partition	VERB
ejpam-5611	90	16	e.	e.	PROPN
ejpam-5611	90	17	by	by	ADP
ejpam-5611	90	18	(	(	PUNCT
ejpam-5611	90	19	3.3	3.3	NUM
ejpam-5611	90	20	)	)	PUNCT
ejpam-5611	90	21	,	,	PUNCT
ejpam-5611	90	22	{	{	PUNCT
ejpam-5611	90	23	(	(	PUNCT
ejpam-5611	90	24	ψ(η	ψ(η	PROPN
ejpam-5611	90	25	)	)	PUNCT
ejpam-5611	90	26	,	,	PUNCT
ejpam-5611	90	27	ψ(j	ψ(j	NOUN
ejpam-5611	90	28	)	)	PUNCT
ejpam-5611	90	29	)	)	PUNCT
ejpam-5611	90	30	}	}	PUNCT
ejpam-5611	90	31	is	be	AUX
ejpam-5611	90	32	δ1	δ1	NOUN
ejpam-5611	90	33	-	-	PUNCT
ejpam-5611	90	34	fine	fine	ADJ
ejpam-5611	90	35	division	division	NOUN
ejpam-5611	90	36	of	of	ADP
ejpam-5611	90	37	e.	e.	PROPN
ejpam-5611	90	38	thus	thus	ADV
ejpam-5611	90	39	,	,	PUNCT
ejpam-5611	90	40	by	by	ADP
ejpam-5611	90	41	(	(	PUNCT
ejpam-5611	90	42	3.1	3.1	NUM
ejpam-5611	90	43	)	)	PUNCT
ejpam-5611	90	44	ϵ	ϵ	ADP
ejpam-5611	90	45	2	2	NUM
ejpam-5611	90	46	>	>	NOUN
ejpam-5611	90	47	∣∣∣∣(r	∣∣∣∣(r	NOUN
ejpam-5611	90	48	)	)	PUNCT
ejpam-5611	90	49	∫	∫	PROPN
ejpam-5611	91	1	e	e	PROPN
ejpam-5611	91	2	φ	φ	PROPN
ejpam-5611	91	3	dg	dg	PROPN
ejpam-5611	91	4	−	−	PROPN
ejpam-5611	91	5	∑	∑	PROPN
ejpam-5611	91	6	d0	d0	PROPN
ejpam-5611	91	7	φ(ψ(η	φ(ψ(η	NOUN
ejpam-5611	91	8	)	)	PUNCT
ejpam-5611	91	9	)	)	PUNCT
ejpam-5611	91	10	·	·	PUNCT
ejpam-5611	91	11	∆g(ψ(j	∆g(ψ(j	PROPN
ejpam-5611	91	12	)	)	PUNCT
ejpam-5611	91	13	)	)	PUNCT
ejpam-5611	91	14	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5611	91	15	g.	g.	PROPN
ejpam-5611	91	16	flores	flores	PROPN
ejpam-5611	91	17	,	,	PUNCT
ejpam-5611	91	18	a.	a.	PROPN
ejpam-5611	91	19	flores	flores	PROPN
ejpam-5611	91	20	/	/	SYM
ejpam-5611	91	21	eur	eur	PROPN
ejpam-5611	91	22	.	.	PUNCT
ejpam-5611	92	1	j.	j.	PROPN
ejpam-5611	92	2	pure	pure	PROPN
ejpam-5611	92	3	appl	appl	PROPN
ejpam-5611	92	4	.	.	PROPN
ejpam-5611	92	5	math	math	PROPN
ejpam-5611	92	6	,	,	PUNCT
ejpam-5611	92	7	18	18	NUM
ejpam-5611	92	8	(	(	PUNCT
ejpam-5611	92	9	2	2	NUM
ejpam-5611	92	10	)	)	PUNCT
ejpam-5611	92	11	(	(	PUNCT
ejpam-5611	92	12	2025	2025	NUM
ejpam-5611	92	13	)	)	PUNCT
ejpam-5611	92	14	,	,	PUNCT
ejpam-5611	92	15	5611	5611	NUM
ejpam-5611	92	16	5	5	NUM
ejpam-5611	92	17	of	of	ADP
ejpam-5611	92	18	16	16	NUM
ejpam-5611	92	19	=	=	SYM
ejpam-5611	92	20	∣∣∣∣(r	∣∣∣∣(r	NOUN
ejpam-5611	92	21	)	)	PUNCT
ejpam-5611	92	22	∫	∫	PROPN
ejpam-5611	93	1	e	e	PROPN
ejpam-5611	93	2	φ	φ	PROPN
ejpam-5611	93	3	dg	dg	PROPN
ejpam-5611	93	4	−	−	PROPN
ejpam-5611	93	5	∑	∑	PROPN
ejpam-5611	93	6	d0	d0	PROPN
ejpam-5611	93	7	(	(	PUNCT
ejpam-5611	93	8	φ	φ	NOUN
ejpam-5611	93	9	◦	◦	NOUN
ejpam-5611	93	10	ψ)(η	ψ)(η	PROPN
ejpam-5611	93	11	)	)	PUNCT
ejpam-5611	93	12	·	·	PUNCT
ejpam-5611	93	13	∆g	∆g	PROPN
ejpam-5611	93	14	◦	◦	NOUN
ejpam-5611	93	15	ψ(j	ψ(j	NOUN
ejpam-5611	93	16	)	)	PUNCT
ejpam-5611	93	17	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5611	93	18	(	(	PUNCT
ejpam-5611	93	19	3.4	3.4	NUM
ejpam-5611	93	20	)	)	PUNCT
ejpam-5611	93	21	note	note	NOUN
ejpam-5611	93	22	that	that	SCONJ
ejpam-5611	93	23	since	since	SCONJ
ejpam-5611	93	24	δ	δ	PROPN
ejpam-5611	93	25	≤	≤	PUNCT
ejpam-5611	93	26	δ0	δ0	NOUN
ejpam-5611	93	27	,	,	PUNCT
ejpam-5611	93	28	d0	d0	NOUN
ejpam-5611	93	29	is	be	AUX
ejpam-5611	93	30	also	also	ADV
ejpam-5611	93	31	a	a	DET
ejpam-5611	93	32	δ0	δ0	NOUN
ejpam-5611	93	33	-	-	PUNCT
ejpam-5611	93	34	fine	fine	ADJ
ejpam-5611	93	35	division	division	NOUN
ejpam-5611	93	36	of	of	ADP
ejpam-5611	93	37	ψ−1(e	ψ−1(e	PROPN
ejpam-5611	93	38	)	)	PUNCT
ejpam-5611	93	39	.	.	PUNCT
ejpam-5611	94	1	hence	hence	ADV
ejpam-5611	94	2	,	,	PUNCT
ejpam-5611	94	3	by	by	ADP
ejpam-5611	94	4	(	(	PUNCT
ejpam-5611	94	5	3.2)∣∣∣∣∑	3.2)∣∣∣∣∑	NUM
ejpam-5611	94	6	d0	d0	NOUN
ejpam-5611	94	7	(	(	PUNCT
ejpam-5611	94	8	φ	φ	NOUN
ejpam-5611	94	9	◦	◦	NOUN
ejpam-5611	94	10	ψ)(η)∆g	ψ)(η)∆g	NUM
ejpam-5611	94	11	◦	◦	NOUN
ejpam-5611	94	12	ψ(j)−	ψ(j)−	NOUN
ejpam-5611	94	13	(	(	PUNCT
ejpam-5611	94	14	r	r	NOUN
ejpam-5611	94	15	)	)	PUNCT
ejpam-5611	94	16	∫	∫	PROPN
ejpam-5611	94	17	ψ−1(e	ψ−1(e	PROPN
ejpam-5611	94	18	)	)	PUNCT
ejpam-5611	94	19	(	(	PUNCT
ejpam-5611	94	20	φ	φ	NUM
ejpam-5611	94	21	◦	◦	PROPN
ejpam-5611	94	22	ψ)|	ψ)|	PROPN
ejpam-5611	94	23	detψ|	detψ|	NOUN
ejpam-5611	94	24	dg	dg	NOUN
ejpam-5611	94	25	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5611	94	26	<	<	X
ejpam-5611	94	27	ϵ	ϵ	X
ejpam-5611	94	28	2	2	NUM
ejpam-5611	94	29	.	.	PUNCT
ejpam-5611	95	1	(	(	PUNCT
ejpam-5611	95	2	3.5	3.5	NUM
ejpam-5611	95	3	)	)	PUNCT
ejpam-5611	95	4	therefore	therefore	ADV
ejpam-5611	95	5	,	,	PUNCT
ejpam-5611	95	6	by	by	ADP
ejpam-5611	95	7	(	(	PUNCT
ejpam-5611	95	8	3.4	3.4	NUM
ejpam-5611	95	9	)	)	PUNCT
ejpam-5611	95	10	and	and	CCONJ
ejpam-5611	95	11	(	(	PUNCT
ejpam-5611	95	12	3.5	3.5	NUM
ejpam-5611	95	13	)	)	PUNCT
ejpam-5611	95	14	0	0	NUM
ejpam-5611	95	15	≤	≤	NUM
ejpam-5611	95	16	∣∣∣∣(r	∣∣∣∣(r	NOUN
ejpam-5611	95	17	)	)	PUNCT
ejpam-5611	95	18	∫	∫	PROPN
ejpam-5611	96	1	e	e	PROPN
ejpam-5611	96	2	φ	φ	PROPN
ejpam-5611	96	3	dg	dg	PROPN
ejpam-5611	96	4	−	−	PROPN
ejpam-5611	96	5	(	(	PUNCT
ejpam-5611	96	6	r	r	NOUN
ejpam-5611	96	7	)	)	PUNCT
ejpam-5611	96	8	∫	∫	PROPN
ejpam-5611	96	9	ψ−1(e	ψ−1(e	PROPN
ejpam-5611	96	10	)	)	PUNCT
ejpam-5611	96	11	(	(	PUNCT
ejpam-5611	96	12	φ	φ	NUM
ejpam-5611	96	13	◦	◦	NOUN
ejpam-5611	96	14	ψ)|detψ|	ψ)|detψ|	NOUN
ejpam-5611	96	15	dg	dg	VERB
ejpam-5611	96	16	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5611	96	17	=	=	PUNCT
ejpam-5611	96	18	∣∣∣∣(r	∣∣∣∣(r	NOUN
ejpam-5611	96	19	)	)	PUNCT
ejpam-5611	96	20	∫	∫	PROPN
ejpam-5611	97	1	e	e	PROPN
ejpam-5611	97	2	φ	φ	PROPN
ejpam-5611	97	3	dg	dg	PROPN
ejpam-5611	97	4	−	−	PROPN
ejpam-5611	97	5	∑	∑	PROPN
ejpam-5611	97	6	d0	d0	PROPN
ejpam-5611	97	7	(	(	PUNCT
ejpam-5611	97	8	φ	φ	NUM
ejpam-5611	97	9	◦	◦	PROPN
ejpam-5611	97	10	ψ)(t)∆(g	ψ)(t)∆(g	PROPN
ejpam-5611	97	11	◦	◦	NOUN
ejpam-5611	97	12	ψ)(j	ψ)(j	NOUN
ejpam-5611	97	13	)	)	PUNCT
ejpam-5611	98	1	+	+	CCONJ
ejpam-5611	98	2	∑	∑	PROPN
ejpam-5611	98	3	d0	d0	PROPN
ejpam-5611	98	4	(	(	PUNCT
ejpam-5611	98	5	φ	φ	NUM
ejpam-5611	98	6	◦	◦	PROPN
ejpam-5611	98	7	ψ)(t)∆(g	ψ)(t)∆(g	PROPN
ejpam-5611	98	8	◦	◦	PROPN
ejpam-5611	98	9	ψ)(j)−	ψ)(j)−	PROPN
ejpam-5611	98	10	(	(	PUNCT
ejpam-5611	98	11	r	r	NOUN
ejpam-5611	98	12	)	)	PUNCT
ejpam-5611	98	13	∫	∫	PROPN
ejpam-5611	98	14	ψ−1(e	ψ−1(e	PROPN
ejpam-5611	98	15	)	)	PUNCT
ejpam-5611	98	16	(	(	PUNCT
ejpam-5611	98	17	φ	φ	NUM
ejpam-5611	98	18	◦	◦	PROPN
ejpam-5611	98	19	ψ)|	ψ)|	PROPN
ejpam-5611	98	20	detψ|	detψ|	NOUN
ejpam-5611	98	21	dg	dg	NOUN
ejpam-5611	98	22	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5611	98	23	≤	≤	NUM
ejpam-5611	98	24	∣∣∣∣(r	∣∣∣∣(r	NOUN
ejpam-5611	98	25	)	)	PUNCT
ejpam-5611	98	26	∫	∫	PROPN
ejpam-5611	99	1	e	e	PROPN
ejpam-5611	99	2	φ	φ	PROPN
ejpam-5611	99	3	dg	dg	PROPN
ejpam-5611	99	4	−	−	PROPN
ejpam-5611	99	5	∑	∑	PROPN
ejpam-5611	99	6	d0	d0	PROPN
ejpam-5611	99	7	(	(	PUNCT
ejpam-5611	99	8	φ	φ	NUM
ejpam-5611	99	9	◦	◦	PROPN
ejpam-5611	99	10	ψ)(t)∆(g	ψ)(t)∆(g	PROPN
ejpam-5611	99	11	◦	◦	NOUN
ejpam-5611	99	12	ψ)(j	ψ)(j	NOUN
ejpam-5611	99	13	)	)	PUNCT
ejpam-5611	99	14	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5611	99	15	+	+	CCONJ
ejpam-5611	99	16	∣∣∣∣∑	∣∣∣∣∑	PROPN
ejpam-5611	99	17	d0	d0	NOUN
ejpam-5611	99	18	(	(	PUNCT
ejpam-5611	99	19	φ	φ	NUM
ejpam-5611	99	20	◦	◦	PROPN
ejpam-5611	99	21	ψ)(t)∆(g	ψ)(t)∆(g	PROPN
ejpam-5611	99	22	◦	◦	PROPN
ejpam-5611	99	23	ψ)(j)−	ψ)(j)−	PROPN
ejpam-5611	99	24	(	(	PUNCT
ejpam-5611	99	25	r	r	NOUN
ejpam-5611	99	26	)	)	PUNCT
ejpam-5611	99	27	∫	∫	PROPN
ejpam-5611	99	28	ψ−1(e	ψ−1(e	PROPN
ejpam-5611	99	29	)	)	PUNCT
ejpam-5611	99	30	(	(	PUNCT
ejpam-5611	99	31	φ	φ	NUM
ejpam-5611	99	32	◦	◦	NOUN
ejpam-5611	99	33	ψ)|detψ|	ψ)|detψ|	NOUN
ejpam-5611	99	34	dg	dg	VERB
ejpam-5611	99	35	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5611	99	36	<	<	X
ejpam-5611	99	37	ϵ	ϵ	X
ejpam-5611	99	38	2	2	NUM
ejpam-5611	99	39	+	+	CCONJ
ejpam-5611	99	40	ϵ	ϵ	SYM
ejpam-5611	99	41	2	2	NUM
ejpam-5611	99	42	=	=	SYM
ejpam-5611	99	43	ϵ.	ϵ.	NOUN
ejpam-5611	99	44	since	since	SCONJ
ejpam-5611	99	45	ϵ	ϵ	PROPN
ejpam-5611	99	46	>	>	X
ejpam-5611	99	47	0	0	NUM
ejpam-5611	99	48	is	be	AUX
ejpam-5611	99	49	arbitrary	arbitrary	ADJ
ejpam-5611	99	50	,	,	PUNCT
ejpam-5611	99	51	we	we	PRON
ejpam-5611	99	52	have	have	VERB
ejpam-5611	99	53	(	(	PUNCT
ejpam-5611	99	54	r	r	NOUN
ejpam-5611	99	55	)	)	PUNCT
ejpam-5611	99	56	∫	∫	NOUN
ejpam-5611	100	1	e	e	PROPN
ejpam-5611	100	2	φ	φ	PROPN
ejpam-5611	100	3	dg	dg	PROPN
ejpam-5611	101	1	=	=	SYM
ejpam-5611	101	2	(	(	PUNCT
ejpam-5611	101	3	r	r	NOUN
ejpam-5611	101	4	)	)	PUNCT
ejpam-5611	101	5	∫	∫	PROPN
ejpam-5611	101	6	ψ−1(e	ψ−1(e	PROPN
ejpam-5611	101	7	)	)	PUNCT
ejpam-5611	101	8	(	(	PUNCT
ejpam-5611	101	9	φ	φ	NUM
ejpam-5611	101	10	◦	◦	VERB
ejpam-5611	101	11	ψ)|detψ|	ψ)|detψ|	NOUN
ejpam-5611	101	12	dg	dg	NOUN
ejpam-5611	101	13	.	.	PUNCT
ejpam-5611	102	1	□	□	PUNCT
ejpam-5611	102	2	theorem	theorem	NOUN
ejpam-5611	102	3	1	1	NUM
ejpam-5611	102	4	.	.	PUNCT
ejpam-5611	103	1	(	(	PUNCT
ejpam-5611	103	2	change	change	NOUN
ejpam-5611	103	3	of	of	ADP
ejpam-5611	103	4	variable	variable	ADJ
ejpam-5611	103	5	formula	formula	NOUN
ejpam-5611	103	6	)	)	PUNCT
ejpam-5611	103	7	.	.	PUNCT
ejpam-5611	104	1	let	let	VERB
ejpam-5611	104	2	f	f	NOUN
ejpam-5611	104	3	:	:	PUNCT
ejpam-5611	105	1	[	[	X
ejpam-5611	105	2	a	a	X
ejpam-5611	105	3	,	,	PUNCT
ejpam-5611	105	4	b	b	NOUN
ejpam-5611	105	5	]	]	X
ejpam-5611	105	6	→	→	PUNCT
ejpam-5611	105	7	x	x	PUNCT
ejpam-5611	105	8	be	be	VERB
ejpam-5611	105	9	pu	pu	PROPN
ejpam-5611	105	10	integrable	integrable	ADJ
ejpam-5611	105	11	over	over	ADP
ejpam-5611	105	12	[	[	X
ejpam-5611	105	13	a	a	DET
ejpam-5611	105	14	,	,	PUNCT
ejpam-5611	105	15	b	b	NOUN
ejpam-5611	105	16	]	]	PUNCT
ejpam-5611	105	17	.	.	PUNCT
ejpam-5611	106	1	let	let	VERB
ejpam-5611	106	2	u	u	PRON
ejpam-5611	106	3	be	be	AUX
ejpam-5611	106	4	an	an	DET
ejpam-5611	106	5	open	open	ADJ
ejpam-5611	106	6	subset	subset	NOUN
ejpam-5611	106	7	of	of	ADP
ejpam-5611	106	8	a	a	DET
ejpam-5611	106	9	compact	compact	ADJ
ejpam-5611	106	10	interval	interval	NOUN
ejpam-5611	106	11	e	e	NOUN
ejpam-5611	106	12	in	in	ADP
ejpam-5611	106	13	rm	rm	PROPN
ejpam-5611	106	14	.	.	PUNCT
ejpam-5611	107	1	let	let	VERB
ejpam-5611	107	2	ψ	ψ	X
ejpam-5611	107	3	:	:	PUNCT
ejpam-5611	107	4	u	u	X
ejpam-5611	107	5	→	→	SYM
ejpam-5611	107	6	ψ(u	ψ(u	PROPN
ejpam-5611	107	7	)	)	PUNCT
ejpam-5611	107	8	be	be	VERB
ejpam-5611	107	9	c1	c1	NOUN
ejpam-5611	107	10	-	-	PUNCT
ejpam-5611	107	11	diffeomorphism	diffeomorphism	NOUN
ejpam-5611	107	12	and	and	CCONJ
ejpam-5611	107	13	[	[	X
ejpam-5611	107	14	a	a	X
ejpam-5611	107	15	,	,	PUNCT
ejpam-5611	107	16	b	b	NOUN
ejpam-5611	107	17	]	]	X
ejpam-5611	107	18	⊆	⊆	NUM
ejpam-5611	107	19	ψ(u	ψ(u	PROPN
ejpam-5611	107	20	)	)	PUNCT
ejpam-5611	107	21	⊆	⊆	NUM
ejpam-5611	107	22	rn	rn	PROPN
ejpam-5611	107	23	.	.	PUNCT
ejpam-5611	108	1	then	then	ADV
ejpam-5611	108	2	(	(	PUNCT
ejpam-5611	108	3	f	f	X
ejpam-5611	108	4	◦	◦	NOUN
ejpam-5611	108	5	ψ	ψ	X
ejpam-5611	108	6	)	)	PUNCT
ejpam-5611	108	7	·	·	PUNCT
ejpam-5611	108	8	|detψ|	|detψ|	PROPN
ejpam-5611	108	9	·	·	PUNCT
ejpam-5611	108	10	χψ−1([a	χψ−1([a	PROPN
ejpam-5611	108	11	,	,	PUNCT
ejpam-5611	108	12	b	b	NOUN
ejpam-5611	108	13	]	]	X
ejpam-5611	108	14	)	)	PUNCT
ejpam-5611	108	15	is	be	AUX
ejpam-5611	108	16	pu	pu	PROPN
ejpam-5611	108	17	integrable	integrable	ADJ
ejpam-5611	108	18	over	over	ADP
ejpam-5611	108	19	e	e	PROPN
ejpam-5611	108	20	and	and	CCONJ
ejpam-5611	109	1	(	(	PUNCT
ejpam-5611	109	2	p	p	NOUN
ejpam-5611	109	3	)	)	PUNCT
ejpam-5611	109	4	∫	∫	PROPN
ejpam-5611	110	1	e	e	X
ejpam-5611	110	2	(	(	PUNCT
ejpam-5611	110	3	f	f	PROPN
ejpam-5611	110	4	◦	◦	NOUN
ejpam-5611	110	5	ψ	ψ	NOUN
ejpam-5611	110	6	)	)	PUNCT
ejpam-5611	110	7	·	·	PUNCT
ejpam-5611	111	1	|	|	ADV
ejpam-5611	111	2	detψ|	detψ|	NOUN
ejpam-5611	111	3	·	·	PUNCT
ejpam-5611	111	4	χψ−1([a	χψ−1([a	PROPN
ejpam-5611	111	5	,	,	PUNCT
ejpam-5611	111	6	b	b	NOUN
ejpam-5611	111	7	]	]	X
ejpam-5611	111	8	)	)	PUNCT
ejpam-5611	111	9	=	=	SYM
ejpam-5611	112	1	(	(	PUNCT
ejpam-5611	112	2	p	p	NOUN
ejpam-5611	112	3	)	)	PUNCT
ejpam-5611	112	4	∫	∫	PROPN
ejpam-5611	112	5	ψ−1([a	ψ−1([a	PROPN
ejpam-5611	112	6	,	,	PUNCT
ejpam-5611	112	7	b	b	NOUN
ejpam-5611	112	8	]	]	X
ejpam-5611	112	9	)	)	PUNCT
ejpam-5611	112	10	(	(	PUNCT
ejpam-5611	112	11	f	f	X
ejpam-5611	112	12	◦	◦	NOUN
ejpam-5611	112	13	ψ	ψ	NOUN
ejpam-5611	112	14	)	)	PUNCT
ejpam-5611	112	15	·	·	PUNCT
ejpam-5611	113	1	|	|	ADV
ejpam-5611	113	2	detψ|	detψ|	NOUN
ejpam-5611	113	3	=	=	SYM
ejpam-5611	113	4	(	(	PUNCT
ejpam-5611	113	5	p	p	NOUN
ejpam-5611	113	6	)	)	PUNCT
ejpam-5611	113	7	∫	∫	PROPN
ejpam-5611	114	1	[	[	X
ejpam-5611	114	2	a	a	X
ejpam-5611	114	3	,	,	PUNCT
ejpam-5611	114	4	b	b	NOUN
ejpam-5611	114	5	]	]	X
ejpam-5611	114	6	f.	f.	NOUN
ejpam-5611	114	7	proof	proof	NOUN
ejpam-5611	114	8	:	:	PUNCT
ejpam-5611	114	9	fix	fix	VERB
ejpam-5611	114	10	ϵ	ϵ	X
ejpam-5611	114	11	>	>	X
ejpam-5611	114	12	0	0	NUM
ejpam-5611	114	13	.	.	PUNCT
ejpam-5611	115	1	since	since	SCONJ
ejpam-5611	115	2	f	f	PROPN
ejpam-5611	115	3	is	be	AUX
ejpam-5611	115	4	pu	pu	PROPN
ejpam-5611	115	5	integrable	integrable	ADJ
ejpam-5611	115	6	over	over	ADP
ejpam-5611	115	7	[	[	X
ejpam-5611	115	8	a	a	DET
ejpam-5611	115	9	,	,	PUNCT
ejpam-5611	115	10	b	b	NOUN
ejpam-5611	115	11	]	]	X
ejpam-5611	115	12	,	,	PUNCT
ejpam-5611	115	13	we	we	PRON
ejpam-5611	115	14	choose	choose	VERB
ejpam-5611	115	15	a	a	DET
ejpam-5611	115	16	gauge	gauge	ADJ
ejpam-5611	115	17	δ0	δ0	NOUN
ejpam-5611	115	18	on	on	ADP
ejpam-5611	115	19	[	[	X
ejpam-5611	115	20	a	a	DET
ejpam-5611	115	21	,	,	PUNCT
ejpam-5611	115	22	b	b	NOUN
ejpam-5611	115	23	]	]	X
ejpam-5611	115	24	such	such	ADJ
ejpam-5611	115	25	that	that	SCONJ
ejpam-5611	115	26	∥∥∥∥∑	∥∥∥∥∑	PROPN
ejpam-5611	115	27	d	d	ADJ
ejpam-5611	115	28	f(ξ	f(ξ	NOUN
ejpam-5611	115	29	)	)	PUNCT
ejpam-5611	115	30	∫	∫	NOUN
ejpam-5611	116	1	i	i	PRON
ejpam-5611	116	2	φ−	φ−	PROPN
ejpam-5611	116	3	(	(	PUNCT
ejpam-5611	116	4	p	p	NOUN
ejpam-5611	116	5	)	)	PUNCT
ejpam-5611	116	6	∫	∫	PROPN
ejpam-5611	117	1	[	[	X
ejpam-5611	117	2	a	a	X
ejpam-5611	117	3	,	,	PUNCT
ejpam-5611	117	4	b	b	NOUN
ejpam-5611	117	5	]	]	X
ejpam-5611	117	6	f	f	X
ejpam-5611	117	7	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5611	117	8	<	<	X
ejpam-5611	117	9	ϵ	ϵ	X
ejpam-5611	117	10	2	2	NUM
ejpam-5611	117	11	g.	g.	NOUN
ejpam-5611	117	12	flores	flore	NOUN
ejpam-5611	117	13	,	,	PUNCT
ejpam-5611	117	14	a.	a.	PROPN
ejpam-5611	117	15	flores	flores	PROPN
ejpam-5611	117	16	/	/	SYM
ejpam-5611	117	17	eur	eur	PROPN
ejpam-5611	117	18	.	.	PUNCT
ejpam-5611	118	1	j.	j.	PROPN
ejpam-5611	118	2	pure	pure	PROPN
ejpam-5611	118	3	appl	appl	PROPN
ejpam-5611	118	4	.	.	PROPN
ejpam-5611	118	5	math	math	PROPN
ejpam-5611	118	6	,	,	PUNCT
ejpam-5611	118	7	18	18	NUM
ejpam-5611	118	8	(	(	PUNCT
ejpam-5611	118	9	2	2	NUM
ejpam-5611	118	10	)	)	PUNCT
ejpam-5611	118	11	(	(	PUNCT
ejpam-5611	118	12	2025	2025	NUM
ejpam-5611	118	13	)	)	PUNCT
ejpam-5611	118	14	,	,	PUNCT
ejpam-5611	118	15	5611	5611	NUM
ejpam-5611	118	16	6	6	NUM
ejpam-5611	118	17	of	of	ADP
ejpam-5611	118	18	16	16	NUM
ejpam-5611	118	19	for	for	ADP
ejpam-5611	118	20	every	every	DET
ejpam-5611	118	21	δ0	δ0	NOUN
ejpam-5611	118	22	-	-	PUNCT
ejpam-5611	118	23	fine	fine	NOUN
ejpam-5611	118	24	division	division	NOUN
ejpam-5611	118	25	d	d	NOUN
ejpam-5611	118	26	=	=	PRON
ejpam-5611	118	27	{	{	PUNCT
ejpam-5611	118	28	(	(	PUNCT
ejpam-5611	118	29	ξ	ξ	PROPN
ejpam-5611	118	30	,	,	PUNCT
ejpam-5611	118	31	φ	φ	PROPN
ejpam-5611	118	32	,	,	PUNCT
ejpam-5611	118	33	i	i	NOUN
ejpam-5611	118	34	)	)	PUNCT
ejpam-5611	118	35	}	}	PUNCT
ejpam-5611	118	36	of	of	ADP
ejpam-5611	118	37	[	[	X
ejpam-5611	118	38	a	a	X
ejpam-5611	118	39	,	,	PUNCT
ejpam-5611	118	40	b	b	NOUN
ejpam-5611	118	41	]	]	X
ejpam-5611	118	42	.	.	PUNCT
ejpam-5611	119	1	since	since	SCONJ
ejpam-5611	119	2	ψ	ψ	NOUN
ejpam-5611	119	3	is	be	AUX
ejpam-5611	119	4	a	a	DET
ejpam-5611	119	5	c1	c1	NOUN
ejpam-5611	119	6	-	-	PUNCT
ejpam-5611	119	7	diffeomorphism	diffeomorphism	NOUN
ejpam-5611	119	8	and	and	CCONJ
ejpam-5611	119	9	u	u	NOUN
ejpam-5611	119	10	is	be	AUX
ejpam-5611	119	11	an	an	DET
ejpam-5611	119	12	open	open	ADJ
ejpam-5611	119	13	set	set	NOUN
ejpam-5611	119	14	in	in	ADP
ejpam-5611	119	15	rr	rr	PROPN
ejpam-5611	119	16	,	,	PUNCT
ejpam-5611	119	17	ψ(u	ψ(u	PROPN
ejpam-5611	119	18	)	)	PUNCT
ejpam-5611	119	19	is	be	AUX
ejpam-5611	119	20	open	open	ADJ
ejpam-5611	119	21	in	in	ADP
ejpam-5611	119	22	rn	rn	PROPN
ejpam-5611	119	23	.	.	PUNCT
ejpam-5611	120	1	so	so	ADV
ejpam-5611	120	2	,	,	PUNCT
ejpam-5611	120	3	choose	choose	VERB
ejpam-5611	120	4	δ0	δ0	NOUN
ejpam-5611	120	5	in	in	ADP
ejpam-5611	120	6	such	such	DET
ejpam-5611	120	7	a	a	DET
ejpam-5611	120	8	way	way	NOUN
ejpam-5611	120	9	that	that	PRON
ejpam-5611	120	10	for	for	ADP
ejpam-5611	120	11	each	each	DET
ejpam-5611	120	12	ξ	ξ	PROPN
ejpam-5611	120	13	∈	∈	PROPN
ejpam-5611	120	14	ψ(u	ψ(u	PROPN
ejpam-5611	120	15	)	)	PUNCT
ejpam-5611	120	16	,	,	PUNCT
ejpam-5611	120	17	b(ξ	b(ξ	NOUN
ejpam-5611	120	18	,	,	PUNCT
ejpam-5611	120	19	δ0(ξ	δ0(ξ	NOUN
ejpam-5611	120	20	)	)	PUNCT
ejpam-5611	120	21	)	)	PUNCT
ejpam-5611	121	1	⊆	⊆	NUM
ejpam-5611	121	2	ψ(u	ψ(u	PROPN
ejpam-5611	121	3	)	)	PUNCT
ejpam-5611	121	4	.	.	PUNCT
ejpam-5611	122	1	define	define	VERB
ejpam-5611	122	2	δ	δ	PROPN
ejpam-5611	122	3	:	:	PUNCT
ejpam-5611	122	4	e	e	X
ejpam-5611	122	5	→	→	PUNCT
ejpam-5611	122	6	r+	r+	NOUN
ejpam-5611	122	7	such	such	ADJ
ejpam-5611	122	8	that	that	PRON
ejpam-5611	122	9	for	for	ADP
ejpam-5611	122	10	u	u	PROPN
ejpam-5611	122	11	∈	∈	PROPN
ejpam-5611	122	12	ψ−1([a	ψ−1([a	PROPN
ejpam-5611	122	13	,	,	PUNCT
ejpam-5611	122	14	b	b	NOUN
ejpam-5611	122	15	]	]	X
ejpam-5611	122	16	)	)	PUNCT
ejpam-5611	122	17	,	,	PUNCT
ejpam-5611	122	18	we	we	PRON
ejpam-5611	122	19	have	have	VERB
ejpam-5611	122	20	b(u	b(u	PROPN
ejpam-5611	122	21	,	,	PUNCT
ejpam-5611	122	22	δ(u	δ(u	PROPN
ejpam-5611	122	23	)	)	PUNCT
ejpam-5611	122	24	)	)	PUNCT
ejpam-5611	123	1	⊆	⊆	X
ejpam-5611	123	2	ψ−1	ψ−1	PROPN
ejpam-5611	123	3	(	(	PUNCT
ejpam-5611	123	4	b	b	PROPN
ejpam-5611	123	5	(	(	PUNCT
ejpam-5611	123	6	ψ(u	ψ(u	PROPN
ejpam-5611	123	7	)	)	PUNCT
ejpam-5611	123	8	,	,	PUNCT
ejpam-5611	123	9	δ0(ψ(u	δ0(ψ(u	NOUN
ejpam-5611	123	10	)	)	PUNCT
ejpam-5611	123	11	)	)	PUNCT
ejpam-5611	123	12	2	2	NUM
ejpam-5611	123	13	√	√	PROPN
ejpam-5611	123	14	p	p	NOUN
ejpam-5611	123	15	)	)	PUNCT
ejpam-5611	123	16	)	)	PUNCT
ejpam-5611	123	17	,	,	PUNCT
ejpam-5611	123	18	(	(	PUNCT
ejpam-5611	123	19	3.6	3.6	NUM
ejpam-5611	123	20	)	)	PUNCT
ejpam-5611	123	21	where	where	SCONJ
ejpam-5611	123	22	1	1	NUM
ejpam-5611	123	23	≤	≤	NOUN
ejpam-5611	123	24	p	p	NOUN
ejpam-5611	123	25	is	be	AUX
ejpam-5611	123	26	a	a	DET
ejpam-5611	123	27	fixed	fix	VERB
ejpam-5611	123	28	positive	positive	ADJ
ejpam-5611	123	29	real	real	ADJ
ejpam-5611	123	30	number	number	NOUN
ejpam-5611	123	31	;	;	PUNCT
ejpam-5611	123	32	also	also	ADV
ejpam-5611	123	33	,	,	PUNCT
ejpam-5611	123	34	for	for	ADP
ejpam-5611	123	35	u	u	PROPN
ejpam-5611	123	36	∈	∈	PROPN
ejpam-5611	123	37	e	e	PROPN
ejpam-5611	123	38	\ψ−1([a	\ψ−1([a	PROPN
ejpam-5611	123	39	,	,	PUNCT
ejpam-5611	123	40	b	b	NOUN
ejpam-5611	123	41	]	]	X
ejpam-5611	123	42	)	)	PUNCT
ejpam-5611	123	43	,	,	PUNCT
ejpam-5611	123	44	b(u	b(u	PROPN
ejpam-5611	123	45	,	,	PUNCT
ejpam-5611	123	46	δ(u	δ(u	PROPN
ejpam-5611	123	47	)	)	PUNCT
ejpam-5611	123	48	)	)	PUNCT
ejpam-5611	123	49	∩e	∩e	PUNCT
ejpam-5611	124	1	⊆	⊆	NUM
ejpam-5611	124	2	e	e	NOUN
ejpam-5611	124	3	∖ψ−1([a	∖ψ−1([a	NOUN
ejpam-5611	124	4	,	,	PUNCT
ejpam-5611	124	5	b	b	NOUN
ejpam-5611	124	6	]	]	X
ejpam-5611	124	7	)	)	PUNCT
ejpam-5611	124	8	.	.	PUNCT
ejpam-5611	125	1	(	(	PUNCT
ejpam-5611	125	2	3.7	3.7	NUM
ejpam-5611	125	3	)	)	PUNCT
ejpam-5611	125	4	let	let	VERB
ejpam-5611	125	5	d	d	NOUN
ejpam-5611	125	6	=	=	PRON
ejpam-5611	125	7	{	{	PUNCT
ejpam-5611	125	8	(	(	PUNCT
ejpam-5611	125	9	ξ	ξ	X
ejpam-5611	125	10	,	,	PUNCT
ejpam-5611	125	11	i	i	PRON
ejpam-5611	125	12	,	,	PUNCT
ejpam-5611	125	13	φ	φ	PROPN
ejpam-5611	125	14	)	)	PUNCT
ejpam-5611	125	15	}	}	PUNCT
ejpam-5611	125	16	be	be	AUX
ejpam-5611	125	17	a	a	DET
ejpam-5611	125	18	δ	δ	NOUN
ejpam-5611	125	19	-	-	PUNCT
ejpam-5611	125	20	fine	fine	ADJ
ejpam-5611	125	21	division	division	NOUN
ejpam-5611	125	22	of	of	ADP
ejpam-5611	125	23	e.	e.	PROPN
ejpam-5611	125	24	suppose	suppose	VERB
ejpam-5611	125	25	d	d	X
ejpam-5611	125	26	=	=	SYM
ejpam-5611	125	27	d1	d1	PROPN
ejpam-5611	125	28	∪	∪	X
ejpam-5611	125	29	d2	d2	PROPN
ejpam-5611	125	30	where	where	SCONJ
ejpam-5611	125	31	d1	d1	PROPN
ejpam-5611	125	32	=	=	SYM
ejpam-5611	125	33	{	{	PUNCT
ejpam-5611	125	34	(	(	PUNCT
ejpam-5611	125	35	ξ	ξ	X
ejpam-5611	125	36	,	,	PUNCT
ejpam-5611	125	37	i	i	PRON
ejpam-5611	125	38	,	,	PUNCT
ejpam-5611	125	39	φ	φ	PROPN
ejpam-5611	125	40	)	)	PUNCT
ejpam-5611	125	41	∈	∈	PROPN
ejpam-5611	125	42	d	d	NOUN
ejpam-5611	125	43	:	:	PUNCT
ejpam-5611	125	44	ξ	ξ	PROPN
ejpam-5611	125	45	∈	∈	PROPN
ejpam-5611	125	46	ψ−1([a	ψ−1([a	PROPN
ejpam-5611	125	47	,	,	PUNCT
ejpam-5611	125	48	b	b	NOUN
ejpam-5611	125	49	]	]	X
ejpam-5611	125	50	)	)	PUNCT
ejpam-5611	125	51	}	}	PUNCT
ejpam-5611	125	52	and	and	CCONJ
ejpam-5611	125	53	d2	d2	PROPN
ejpam-5611	125	54	=	=	SYM
ejpam-5611	126	1	d	d	NOUN
ejpam-5611	126	2	∖d1	∖d1	PROPN
ejpam-5611	126	3	.	.	PUNCT
ejpam-5611	127	1	we	we	PRON
ejpam-5611	127	2	may	may	AUX
ejpam-5611	127	3	assume	assume	VERB
ejpam-5611	127	4	that	that	SCONJ
ejpam-5611	127	5	d1	d1	PROPN
ejpam-5611	127	6	=	=	PUNCT
ejpam-5611	127	7	{	{	PUNCT
ejpam-5611	127	8	(	(	PUNCT
ejpam-5611	127	9	ξk	ξk	ADP
ejpam-5611	127	10	,	,	PUNCT
ejpam-5611	127	11	ik	ik	PROPN
ejpam-5611	127	12	,	,	PUNCT
ejpam-5611	127	13	φk)}rk=1	φk)}rk=1	PROPN
ejpam-5611	127	14	and	and	CCONJ
ejpam-5611	127	15	d2	d2	PROPN
ejpam-5611	127	16	=	=	SYM
ejpam-5611	127	17	{	{	PUNCT
ejpam-5611	127	18	(	(	PUNCT
ejpam-5611	127	19	ξk	ξk	ADP
ejpam-5611	127	20	,	,	PUNCT
ejpam-5611	127	21	ik	ik	PROPN
ejpam-5611	127	22	,	,	PUNCT
ejpam-5611	127	23	φk)}sk	φk)}sk	PROPN
ejpam-5611	127	24	=	=	PROPN
ejpam-5611	127	25	r+1	r+1	PROPN
ejpam-5611	127	26	.	.	PUNCT
ejpam-5611	128	1	let	let	VERB
ejpam-5611	128	2	k	k	PROPN
ejpam-5611	128	3	∈	∈	PROPN
ejpam-5611	128	4	{	{	PUNCT
ejpam-5611	128	5	r	r	NOUN
ejpam-5611	128	6	+	+	NOUN
ejpam-5611	128	7	1	1	NUM
ejpam-5611	128	8	,	,	PUNCT
ejpam-5611	128	9	r	r	NOUN
ejpam-5611	128	10	+	+	PROPN
ejpam-5611	128	11	2	2	NUM
ejpam-5611	128	12	,	,	PUNCT
ejpam-5611	128	13	·	·	PUNCT
ejpam-5611	128	14	·	·	PUNCT
ejpam-5611	128	15	·	·	PUNCT
ejpam-5611	128	16	,	,	PUNCT
ejpam-5611	128	17	s	s	X
ejpam-5611	128	18	}	}	PUNCT
ejpam-5611	128	19	and	and	CCONJ
ejpam-5611	128	20	let	let	VERB
ejpam-5611	128	21	x	x	X
ejpam-5611	128	22	∈	∈	PROPN
ejpam-5611	128	23	supp	supp	PROPN
ejpam-5611	128	24	φk	φk	ADP
ejpam-5611	128	25	.	.	PROPN
ejpam-5611	128	26	here	here	ADV
ejpam-5611	128	27	,	,	PUNCT
ejpam-5611	128	28	φk(x	φk(x	NOUN
ejpam-5611	128	29	)	)	PUNCT
ejpam-5611	128	30	>	>	X
ejpam-5611	128	31	0	0	X
ejpam-5611	128	32	.	.	PUNCT
ejpam-5611	129	1	since	since	SCONJ
ejpam-5611	129	2	d	d	PROPN
ejpam-5611	129	3	is	be	AUX
ejpam-5611	129	4	a	a	DET
ejpam-5611	129	5	δ	δ	NOUN
ejpam-5611	129	6	-	-	PUNCT
ejpam-5611	129	7	fine	fine	ADJ
ejpam-5611	129	8	division	division	NOUN
ejpam-5611	129	9	of	of	ADP
ejpam-5611	129	10	e	e	PROPN
ejpam-5611	129	11	,	,	PUNCT
ejpam-5611	129	12	supp	supp	NOUN
ejpam-5611	129	13	φk	φk	ADP
ejpam-5611	129	14	⊆	⊆	NUM
ejpam-5611	129	15	ik	ik	PROPN
ejpam-5611	129	16	⊆	⊆	NUM
ejpam-5611	129	17	b(ξk	b(ξk	PROPN
ejpam-5611	129	18	,	,	PUNCT
ejpam-5611	129	19	δ(ξk	δ(ξk	NOUN
ejpam-5611	129	20	)	)	PUNCT
ejpam-5611	129	21	)	)	PUNCT
ejpam-5611	129	22	;	;	PUNCT
ejpam-5611	129	23	which	which	PRON
ejpam-5611	129	24	implies	imply	VERB
ejpam-5611	129	25	supp	supp	NOUN
ejpam-5611	129	26	φk	φk	ADP
ejpam-5611	129	27	=	=	SYM
ejpam-5611	129	28	supp	supp	PROPN
ejpam-5611	129	29	φk	φk	ADP
ejpam-5611	129	30	∩e	∩e	PROPN
ejpam-5611	129	31	⊆	⊆	NUM
ejpam-5611	129	32	b(ξk	b(ξk	PROPN
ejpam-5611	129	33	,	,	PUNCT
ejpam-5611	129	34	δ(ξk	δ(ξk	NOUN
ejpam-5611	129	35	)	)	PUNCT
ejpam-5611	129	36	)	)	PUNCT
ejpam-5611	130	1	∩e	∩e	PROPN
ejpam-5611	130	2	.	.	PUNCT
ejpam-5611	131	1	and	and	CCONJ
ejpam-5611	131	2	by	by	ADP
ejpam-5611	131	3	(	(	PUNCT
ejpam-5611	131	4	3.7	3.7	NUM
ejpam-5611	131	5	)	)	PUNCT
ejpam-5611	131	6	,	,	PUNCT
ejpam-5611	131	7	supp	supp	NOUN
ejpam-5611	131	8	φk	φk	ADP
ejpam-5611	131	9	⊆	⊆	NUM
ejpam-5611	131	10	b(ξk	b(ξk	PROPN
ejpam-5611	131	11	,	,	PUNCT
ejpam-5611	131	12	δ(ξk	δ(ξk	NOUN
ejpam-5611	131	13	)	)	PUNCT
ejpam-5611	131	14	)	)	PUNCT
ejpam-5611	132	1	∩e	∩e	PUNCT
ejpam-5611	133	1	⊆	⊆	NUM
ejpam-5611	133	2	e	e	PROPN
ejpam-5611	133	3	\ψ−1([a	\ψ−1([a	PROPN
ejpam-5611	133	4	,	,	PUNCT
ejpam-5611	133	5	b	b	NOUN
ejpam-5611	133	6	]	]	X
ejpam-5611	133	7	)	)	PUNCT
ejpam-5611	133	8	;	;	PUNCT
ejpam-5611	133	9	which	which	PRON
ejpam-5611	133	10	means	mean	VERB
ejpam-5611	133	11	supp	supp	PROPN
ejpam-5611	133	12	φk	φk	ADP
ejpam-5611	133	13	∩	∩	ADJ
ejpam-5611	133	14	ψ−1([a	ψ−1([a	PROPN
ejpam-5611	133	15	,	,	PUNCT
ejpam-5611	133	16	b	b	NOUN
ejpam-5611	133	17	]	]	X
ejpam-5611	133	18	)	)	PUNCT
ejpam-5611	133	19	=	=	PUNCT
ejpam-5611	133	20	∅.	∅.	VERB
ejpam-5611	133	21	thus	thus	ADV
ejpam-5611	133	22	,	,	PUNCT
ejpam-5611	133	23	for	for	ADP
ejpam-5611	133	24	each	each	DET
ejpam-5611	133	25	x	x	SYM
ejpam-5611	133	26	∈	∈	PROPN
ejpam-5611	133	27	ψ−1([a	ψ−1([a	PROPN
ejpam-5611	133	28	,	,	PUNCT
ejpam-5611	133	29	b	b	NOUN
ejpam-5611	133	30	]	]	X
ejpam-5611	133	31	)	)	PUNCT
ejpam-5611	133	32	,	,	PUNCT
ejpam-5611	133	33	φk(x	φk(x	NOUN
ejpam-5611	133	34	)	)	PUNCT
ejpam-5611	133	35	=	=	SYM
ejpam-5611	133	36	0	0	NUM
ejpam-5611	133	37	for	for	ADP
ejpam-5611	133	38	all	all	PRON
ejpam-5611	133	39	k	k	NOUN
ejpam-5611	133	40	=	=	PUNCT
ejpam-5611	134	1	r	r	NOUN
ejpam-5611	134	2	+	+	NUM
ejpam-5611	134	3	1	1	NUM
ejpam-5611	134	4	,	,	PUNCT
ejpam-5611	134	5	r	r	NOUN
ejpam-5611	134	6	+	+	PROPN
ejpam-5611	134	7	2	2	NUM
ejpam-5611	134	8	·	·	PUNCT
ejpam-5611	134	9	·	·	PUNCT
ejpam-5611	134	10	·	·	PUNCT
ejpam-5611	134	11	,	,	PUNCT
ejpam-5611	134	12	s.	s.	PROPN
ejpam-5611	134	13	now	now	ADV
ejpam-5611	134	14	,	,	PUNCT
ejpam-5611	134	15	for	for	ADP
ejpam-5611	134	16	each	each	DET
ejpam-5611	134	17	x	x	SYM
ejpam-5611	134	18	∈	∈	PROPN
ejpam-5611	134	19	ψ−1([a	ψ−1([a	PROPN
ejpam-5611	134	20	,	,	PUNCT
ejpam-5611	134	21	b	b	NOUN
ejpam-5611	134	22	]	]	X
ejpam-5611	134	23	)	)	PUNCT
ejpam-5611	134	24	s∑	s∑	PROPN
ejpam-5611	135	1	k	k	X
ejpam-5611	136	1	=	=	PROPN
ejpam-5611	136	2	r+1	r+1	PROPN
ejpam-5611	136	3	φk(x	φk(x	NOUN
ejpam-5611	136	4	)	)	PUNCT
ejpam-5611	136	5	=	=	SYM
ejpam-5611	136	6	0	0	PUNCT
ejpam-5611	137	1	and	and	CCONJ
ejpam-5611	137	2	so	so	ADV
ejpam-5611	137	3	s∑	s∑	PROPN
ejpam-5611	137	4	k=1	k=1	PROPN
ejpam-5611	137	5	φk(x	φk(x	NOUN
ejpam-5611	137	6	)	)	PUNCT
ejpam-5611	137	7	=	=	SYM
ejpam-5611	137	8	r∑	r∑	NOUN
ejpam-5611	137	9	k=1	k=1	X
ejpam-5611	137	10	φk(x	φk(x	PUNCT
ejpam-5611	137	11	)	)	PUNCT
ejpam-5611	138	1	+	+	CCONJ
ejpam-5611	138	2	s∑	s∑	PROPN
ejpam-5611	138	3	k	k	X
ejpam-5611	139	1	=	=	PROPN
ejpam-5611	139	2	r+1	r+1	PROPN
ejpam-5611	139	3	φk(x	φk(x	NOUN
ejpam-5611	139	4	)	)	PUNCT
ejpam-5611	139	5	=	=	SYM
ejpam-5611	139	6	r∑	r∑	NOUN
ejpam-5611	139	7	k=1	k=1	ADJ
ejpam-5611	139	8	φk(x	φk(x	NOUN
ejpam-5611	139	9	)	)	PUNCT
ejpam-5611	139	10	.	.	PUNCT
ejpam-5611	140	1	for	for	ADP
ejpam-5611	140	2	each	each	PRON
ejpam-5611	140	3	k	k	NOUN
ejpam-5611	140	4	=	=	SYM
ejpam-5611	140	5	1	1	NUM
ejpam-5611	140	6	,	,	PUNCT
ejpam-5611	140	7	2	2	NUM
ejpam-5611	140	8	,	,	PUNCT
ejpam-5611	140	9	·	·	PUNCT
ejpam-5611	140	10	·	·	PUNCT
ejpam-5611	140	11	·	·	PUNCT
ejpam-5611	140	12	r	r	AUX
ejpam-5611	140	13	,	,	PUNCT
ejpam-5611	140	14	let	let	VERB
ejpam-5611	140	15	xk	xk	PROPN
ejpam-5611	140	16	=	=	SYM
ejpam-5611	140	17	ψ(ξk	ψ(ξk	PROPN
ejpam-5611	140	18	)	)	PUNCT
ejpam-5611	140	19	and	and	CCONJ
ejpam-5611	141	1	σk	σk	ADV
ejpam-5611	141	2	=	=	SYM
ejpam-5611	141	3	φk	φk	ADP
ejpam-5611	141	4	◦	◦	NOUN
ejpam-5611	141	5	ψ−1	ψ−1	PROPN
ejpam-5611	141	6	.	.	PUNCT
ejpam-5611	141	7	note	note	NOUN
ejpam-5611	141	8	that	that	PRON
ejpam-5611	141	9	σj	σj	VERB
ejpam-5611	141	10	:	:	PUNCT
ejpam-5611	141	11	ψ(u	ψ(u	PROPN
ejpam-5611	141	12	)	)	PUNCT
ejpam-5611	141	13	→	→	SYM
ejpam-5611	142	1	r	r	NOUN
ejpam-5611	142	2	and	and	CCONJ
ejpam-5611	142	3	b	b	PROPN
ejpam-5611	142	4	(	(	PUNCT
ejpam-5611	142	5	σk(ψ(y	σk(ψ(y	NOUN
ejpam-5611	142	6	)	)	PUNCT
ejpam-5611	142	7	)	)	PUNCT
ejpam-5611	142	8	,	,	PUNCT
ejpam-5611	142	9	δ0(ψ(y	δ0(ψ(y	NOUN
ejpam-5611	142	10	)	)	PUNCT
ejpam-5611	142	11	)	)	PUNCT
ejpam-5611	142	12	2	2	NUM
ejpam-5611	142	13	√	√	PROPN
ejpam-5611	142	14	p	p	NOUN
ejpam-5611	142	15	)	)	PUNCT
ejpam-5611	142	16	⊆	⊆	NUM
ejpam-5611	142	17	b	b	PROPN
ejpam-5611	142	18	(	(	PUNCT
ejpam-5611	142	19	σk(ψ(y	σk(ψ(y	NOUN
ejpam-5611	142	20	)	)	PUNCT
ejpam-5611	142	21	)	)	PUNCT
ejpam-5611	142	22	,	,	PUNCT
ejpam-5611	142	23	δ0(ψ(y	δ0(ψ(y	NOUN
ejpam-5611	142	24	)	)	PUNCT
ejpam-5611	142	25	)	)	PUNCT
ejpam-5611	142	26	)	)	PUNCT
ejpam-5611	142	27	.	.	PUNCT
ejpam-5611	143	1	g.	g.	PROPN
ejpam-5611	143	2	flores	flores	PROPN
ejpam-5611	143	3	,	,	PUNCT
ejpam-5611	143	4	a.	a.	PROPN
ejpam-5611	143	5	flores	flores	PROPN
ejpam-5611	143	6	/	/	SYM
ejpam-5611	143	7	eur	eur	PROPN
ejpam-5611	143	8	.	.	PUNCT
ejpam-5611	144	1	j.	j.	PROPN
ejpam-5611	144	2	pure	pure	PROPN
ejpam-5611	144	3	appl	appl	PROPN
ejpam-5611	144	4	.	.	PROPN
ejpam-5611	144	5	math	math	PROPN
ejpam-5611	144	6	,	,	PUNCT
ejpam-5611	144	7	18	18	NUM
ejpam-5611	144	8	(	(	PUNCT
ejpam-5611	144	9	2	2	NUM
ejpam-5611	144	10	)	)	PUNCT
ejpam-5611	144	11	(	(	PUNCT
ejpam-5611	144	12	2025	2025	NUM
ejpam-5611	144	13	)	)	PUNCT
ejpam-5611	144	14	,	,	PUNCT
ejpam-5611	144	15	5611	5611	NUM
ejpam-5611	144	16	7	7	NUM
ejpam-5611	144	17	of	of	ADP
ejpam-5611	144	18	16	16	NUM
ejpam-5611	144	19	notice	notice	NOUN
ejpam-5611	144	20	that	that	SCONJ
ejpam-5611	144	21	x	x	PUNCT
ejpam-5611	144	22	∈	∈	PROPN
ejpam-5611	144	23	supp	supp	NOUN
ejpam-5611	144	24	σk	σk	PROPN
ejpam-5611	144	25	·	·	PUNCT
ejpam-5611	144	26	χ[a	χ[a	PROPN
ejpam-5611	144	27	,	,	PUNCT
ejpam-5611	144	28	b	b	NOUN
ejpam-5611	144	29	]	]	X
ejpam-5611	144	30	for	for	ADP
ejpam-5611	144	31	all	all	PRON
ejpam-5611	144	32	k	k	NOUN
ejpam-5611	144	33	=	=	SYM
ejpam-5611	144	34	1	1	NUM
ejpam-5611	144	35	,	,	PUNCT
ejpam-5611	144	36	2	2	NUM
ejpam-5611	144	37	,	,	PUNCT
ejpam-5611	144	38	·	·	PUNCT
ejpam-5611	144	39	·	·	PUNCT
ejpam-5611	144	40	·	·	PUNCT
ejpam-5611	144	41	,	,	PUNCT
ejpam-5611	144	42	r	r	NOUN
ejpam-5611	144	43	;	;	PUNCT
ejpam-5611	144	44	then	then	ADV
ejpam-5611	144	45	φk(ψ	φk(ψ	NUM
ejpam-5611	144	46	−1(x	−1(x	NOUN
ejpam-5611	144	47	)	)	PUNCT
ejpam-5611	144	48	)	)	PUNCT
ejpam-5611	144	49	=	=	SYM
ejpam-5611	144	50	(	(	PUNCT
ejpam-5611	144	51	φk	φk	AUX
ejpam-5611	144	52	◦	◦	NOUN
ejpam-5611	144	53	ψ−1)(x	ψ−1)(x	PROPN
ejpam-5611	144	54	)	)	PUNCT
ejpam-5611	144	55	=	=	SYM
ejpam-5611	144	56	σk(x	σk(x	NOUN
ejpam-5611	144	57	)	)	PUNCT
ejpam-5611	144	58	>	>	X
ejpam-5611	145	1	0	0	NUM
ejpam-5611	145	2	,	,	PUNCT
ejpam-5611	145	3	that	that	ADV
ejpam-5611	145	4	is	is	ADV
ejpam-5611	145	5	,	,	PUNCT
ejpam-5611	145	6	ψ−1(x	ψ−1(x	PROPN
ejpam-5611	145	7	)	)	PUNCT
ejpam-5611	145	8	∈	∈	PROPN
ejpam-5611	145	9	supp	supp	PROPN
ejpam-5611	145	10	φk	φk	ADP
ejpam-5611	145	11	.	.	PROPN
ejpam-5611	146	1	from	from	ADP
ejpam-5611	146	2	(	(	PUNCT
ejpam-5611	146	3	3.6	3.6	NUM
ejpam-5611	146	4	)	)	PUNCT
ejpam-5611	146	5	and	and	CCONJ
ejpam-5611	146	6	since	since	SCONJ
ejpam-5611	146	7	d	d	PROPN
ejpam-5611	146	8	is	be	AUX
ejpam-5611	146	9	a	a	DET
ejpam-5611	146	10	δ	δ	NOUN
ejpam-5611	146	11	-	-	PUNCT
ejpam-5611	146	12	fine	fine	ADJ
ejpam-5611	146	13	division	division	NOUN
ejpam-5611	146	14	of	of	ADP
ejpam-5611	146	15	e	e	NOUN
ejpam-5611	146	16	,	,	PUNCT
ejpam-5611	146	17	we	we	PRON
ejpam-5611	146	18	have	have	VERB
ejpam-5611	146	19	ψ−1(x	ψ−1(x	NUM
ejpam-5611	146	20	)	)	PUNCT
ejpam-5611	146	21	∈	∈	PROPN
ejpam-5611	146	22	supp	supp	NOUN
ejpam-5611	146	23	φk	φk	ADP
ejpam-5611	146	24	⊆	⊆	NUM
ejpam-5611	146	25	ik	ik	PROPN
ejpam-5611	146	26	⊆	⊆	NUM
ejpam-5611	146	27	b(ξk	b(ξk	PROPN
ejpam-5611	146	28	,	,	PUNCT
ejpam-5611	146	29	δ(ξk	δ(ξk	NOUN
ejpam-5611	146	30	)	)	PUNCT
ejpam-5611	146	31	)	)	PUNCT
ejpam-5611	147	1	⊆	⊆	X
ejpam-5611	147	2	ψ−1	ψ−1	PROPN
ejpam-5611	147	3	(	(	PUNCT
ejpam-5611	147	4	b	b	PROPN
ejpam-5611	147	5	(	(	PUNCT
ejpam-5611	147	6	ψ(ξk	ψ(ξk	PROPN
ejpam-5611	147	7	)	)	PUNCT
ejpam-5611	147	8	,	,	PUNCT
ejpam-5611	147	9	δ0(ψ(ξk	δ0(ψ(ξk	PROPN
ejpam-5611	147	10	)	)	PUNCT
ejpam-5611	147	11	)	)	PUNCT
ejpam-5611	147	12	2	2	NUM
ejpam-5611	147	13	√	√	NOUN
ejpam-5611	147	14	p	p	NOUN
ejpam-5611	147	15	)	)	PUNCT
ejpam-5611	147	16	)	)	PUNCT
ejpam-5611	147	17	.	.	PUNCT
ejpam-5611	148	1	hence	hence	ADV
ejpam-5611	148	2	,	,	PUNCT
ejpam-5611	148	3	x	x	PUNCT
ejpam-5611	148	4	∈	∈	PROPN
ejpam-5611	148	5	b	b	PROPN
ejpam-5611	148	6	(	(	PUNCT
ejpam-5611	148	7	ψ(ξk	ψ(ξk	PROPN
ejpam-5611	148	8	)	)	PUNCT
ejpam-5611	148	9	,	,	PUNCT
ejpam-5611	148	10	δ0(ψ(ξk	δ0(ψ(ξk	PROPN
ejpam-5611	148	11	)	)	PUNCT
ejpam-5611	148	12	)	)	PUNCT
ejpam-5611	149	1	2	2	NUM
ejpam-5611	149	2	√	√	NOUN
ejpam-5611	149	3	p	p	NOUN
ejpam-5611	149	4	)	)	PUNCT
ejpam-5611	149	5	.	.	PUNCT
ejpam-5611	150	1	thus	thus	ADV
ejpam-5611	150	2	,	,	PUNCT
ejpam-5611	150	3	for	for	ADP
ejpam-5611	150	4	each	each	PRON
ejpam-5611	150	5	k	k	NOUN
ejpam-5611	150	6	=	=	SYM
ejpam-5611	150	7	1	1	NUM
ejpam-5611	150	8	,	,	PUNCT
ejpam-5611	150	9	2	2	NUM
ejpam-5611	150	10	,	,	PUNCT
ejpam-5611	150	11	·	·	PUNCT
ejpam-5611	150	12	·	·	PUNCT
ejpam-5611	150	13	·	·	PUNCT
ejpam-5611	150	14	,	,	PUNCT
ejpam-5611	150	15	r	r	X
ejpam-5611	150	16	,	,	PUNCT
ejpam-5611	150	17	supp	supp	NOUN
ejpam-5611	150	18	σk	σk	ADJ
ejpam-5611	150	19	·	·	PUNCT
ejpam-5611	150	20	χ[a	χ[a	PROPN
ejpam-5611	150	21	,	,	PUNCT
ejpam-5611	150	22	b	b	NOUN
ejpam-5611	150	23	]	]	X
ejpam-5611	150	24	⊆	⊆	NUM
ejpam-5611	150	25	(	(	PUNCT
ejpam-5611	150	26	b	b	PROPN
ejpam-5611	150	27	(	(	PUNCT
ejpam-5611	150	28	ψ(ξk	ψ(ξk	PROPN
ejpam-5611	150	29	)	)	PUNCT
ejpam-5611	150	30	,	,	PUNCT
ejpam-5611	150	31	δ0(ψ(ξk	δ0(ψ(ξk	PROPN
ejpam-5611	150	32	)	)	PUNCT
ejpam-5611	150	33	)	)	PUNCT
ejpam-5611	150	34	2	2	NUM
ejpam-5611	150	35	√	√	PROPN
ejpam-5611	150	36	p	p	NOUN
ejpam-5611	150	37	)	)	PUNCT
ejpam-5611	150	38	)	)	PUNCT
ejpam-5611	150	39	∩	∩	NOUN
ejpam-5611	150	40	[	[	X
ejpam-5611	150	41	a	a	X
ejpam-5611	150	42	,	,	PUNCT
ejpam-5611	150	43	b	b	NOUN
ejpam-5611	150	44	]	]	PUNCT
ejpam-5611	150	45	.	.	PUNCT
ejpam-5611	151	1	now	now	ADV
ejpam-5611	151	2	,	,	PUNCT
ejpam-5611	151	3	since	since	SCONJ
ejpam-5611	151	4	b	b	PROPN
ejpam-5611	151	5	(	(	PUNCT
ejpam-5611	151	6	σk(ψ(y	σk(ψ(y	NOUN
ejpam-5611	151	7	)	)	PUNCT
ejpam-5611	151	8	)	)	PUNCT
ejpam-5611	151	9	,	,	PUNCT
ejpam-5611	151	10	δ0(ψ(y	δ0(ψ(y	NOUN
ejpam-5611	151	11	)	)	PUNCT
ejpam-5611	151	12	)	)	PUNCT
ejpam-5611	151	13	2	2	NUM
ejpam-5611	151	14	√	√	PROPN
ejpam-5611	151	15	p	p	NOUN
ejpam-5611	151	16	)	)	PUNCT
ejpam-5611	151	17	⊆	⊆	NUM
ejpam-5611	151	18	b	b	PROPN
ejpam-5611	151	19	(	(	PUNCT
ejpam-5611	151	20	σk(ψ(y	σk(ψ(y	NOUN
ejpam-5611	151	21	)	)	PUNCT
ejpam-5611	151	22	)	)	PUNCT
ejpam-5611	151	23	,	,	PUNCT
ejpam-5611	151	24	δ0(ψ(y	δ0(ψ(y	NOUN
ejpam-5611	151	25	)	)	PUNCT
ejpam-5611	151	26	)	)	PUNCT
ejpam-5611	151	27	)	)	PUNCT
ejpam-5611	151	28	for	for	ADP
ejpam-5611	151	29	all	all	PRON
ejpam-5611	151	30	k	k	NOUN
ejpam-5611	151	31	=	=	SYM
ejpam-5611	151	32	1	1	NUM
ejpam-5611	151	33	,	,	PUNCT
ejpam-5611	151	34	2	2	NUM
ejpam-5611	151	35	,	,	PUNCT
ejpam-5611	151	36	·	·	PUNCT
ejpam-5611	151	37	·	·	PUNCT
ejpam-5611	151	38	·	·	PUNCT
ejpam-5611	152	1	r	r	X
ejpam-5611	152	2	,	,	PUNCT
ejpam-5611	152	3	it	it	PRON
ejpam-5611	152	4	follows	follow	VERB
ejpam-5611	152	5	that	that	SCONJ
ejpam-5611	152	6	supp	supp	NOUN
ejpam-5611	152	7	σk	σk	ADV
ejpam-5611	152	8	·	·	PUNCT
ejpam-5611	152	9	χ[a	χ[a	PROPN
ejpam-5611	152	10	,	,	PUNCT
ejpam-5611	152	11	b	b	NOUN
ejpam-5611	152	12	]	]	X
ejpam-5611	152	13	⊆	⊆	NUM
ejpam-5611	152	14	b	b	PROPN
ejpam-5611	152	15	(	(	PUNCT
ejpam-5611	152	16	σk(ψ(y	σk(ψ(y	NOUN
ejpam-5611	152	17	)	)	PUNCT
ejpam-5611	152	18	)	)	PUNCT
ejpam-5611	152	19	,	,	PUNCT
ejpam-5611	152	20	δ0(ψ(y	δ0(ψ(y	NOUN
ejpam-5611	152	21	)	)	PUNCT
ejpam-5611	152	22	)	)	PUNCT
ejpam-5611	152	23	2	2	NUM
ejpam-5611	152	24	√	√	PROPN
ejpam-5611	152	25	p	p	NOUN
ejpam-5611	152	26	)	)	PUNCT
ejpam-5611	152	27	∩	∩	NOUN
ejpam-5611	153	1	[	[	X
ejpam-5611	153	2	a	a	PRON
ejpam-5611	153	3	,	,	PUNCT
ejpam-5611	153	4	b	b	NOUN
ejpam-5611	153	5	]	]	X
ejpam-5611	153	6	⊆	⊆	NUM
ejpam-5611	153	7	b	b	PROPN
ejpam-5611	153	8	(	(	PUNCT
ejpam-5611	153	9	σk(ψ(y	σk(ψ(y	NOUN
ejpam-5611	153	10	)	)	PUNCT
ejpam-5611	153	11	)	)	PUNCT
ejpam-5611	153	12	,	,	PUNCT
ejpam-5611	153	13	δ0(ψ(y	δ0(ψ(y	NOUN
ejpam-5611	153	14	)	)	PUNCT
ejpam-5611	153	15	)	)	PUNCT
ejpam-5611	153	16	)	)	PUNCT
ejpam-5611	153	17	∩	∩	NOUN
ejpam-5611	153	18	[	[	X
ejpam-5611	153	19	a	a	X
ejpam-5611	153	20	,	,	PUNCT
ejpam-5611	153	21	b	b	NOUN
ejpam-5611	153	22	]	]	X
ejpam-5611	153	23	for	for	ADP
ejpam-5611	153	24	all	all	PRON
ejpam-5611	153	25	k	k	NOUN
ejpam-5611	153	26	=	=	SYM
ejpam-5611	153	27	1	1	NUM
ejpam-5611	153	28	,	,	PUNCT
ejpam-5611	153	29	2	2	NUM
ejpam-5611	153	30	,	,	PUNCT
ejpam-5611	153	31	·	·	PUNCT
ejpam-5611	153	32	·	·	PUNCT
ejpam-5611	154	1	·	·	PUNCT
ejpam-5611	154	2	r.	r.	PROPN
ejpam-5611	154	3	so	so	ADV
ejpam-5611	154	4	,	,	PUNCT
ejpam-5611	154	5	we	we	PRON
ejpam-5611	154	6	choose	choose	VERB
ejpam-5611	154	7	a	a	DET
ejpam-5611	154	8	compact	compact	ADJ
ejpam-5611	154	9	interval	interval	NOUN
ejpam-5611	154	10	jk	jk	PROPN
ejpam-5611	154	11	such	such	ADJ
ejpam-5611	154	12	that	that	PRON
ejpam-5611	154	13	b	b	X
ejpam-5611	154	14	(	(	PUNCT
ejpam-5611	154	15	σk(ψ(y	σk(ψ(y	NOUN
ejpam-5611	154	16	)	)	PUNCT
ejpam-5611	154	17	)	)	PUNCT
ejpam-5611	154	18	,	,	PUNCT
ejpam-5611	154	19	δ0(ψ(y	δ0(ψ(y	NOUN
ejpam-5611	154	20	)	)	PUNCT
ejpam-5611	154	21	)	)	PUNCT
ejpam-5611	154	22	2	2	NUM
ejpam-5611	154	23	√	√	PROPN
ejpam-5611	154	24	p	p	NOUN
ejpam-5611	154	25	)	)	PUNCT
ejpam-5611	154	26	∩	∩	NOUN
ejpam-5611	155	1	[	[	X
ejpam-5611	155	2	a	a	DET
ejpam-5611	155	3	,	,	PUNCT
ejpam-5611	155	4	b	b	NOUN
ejpam-5611	155	5	]	]	X
ejpam-5611	155	6	⊆	⊆	NUM
ejpam-5611	155	7	jk	jk	PROPN
ejpam-5611	155	8	⊆	⊆	NUM
ejpam-5611	155	9	b	b	PROPN
ejpam-5611	155	10	(	(	PUNCT
ejpam-5611	155	11	σk(ψ(y	σk(ψ(y	NOUN
ejpam-5611	155	12	)	)	PUNCT
ejpam-5611	155	13	)	)	PUNCT
ejpam-5611	155	14	,	,	PUNCT
ejpam-5611	155	15	δ0(ψ(y	δ0(ψ(y	NOUN
ejpam-5611	155	16	)	)	PUNCT
ejpam-5611	155	17	)	)	PUNCT
ejpam-5611	155	18	)	)	PUNCT
ejpam-5611	156	1	∩	∩	NOUN
ejpam-5611	156	2	[	[	X
ejpam-5611	156	3	a	a	X
ejpam-5611	156	4	,	,	PUNCT
ejpam-5611	156	5	b	b	NOUN
ejpam-5611	156	6	]	]	X
ejpam-5611	156	7	.	.	PUNCT
ejpam-5611	157	1	for	for	ADP
ejpam-5611	157	2	all	all	PRON
ejpam-5611	157	3	k	k	NOUN
ejpam-5611	157	4	=	=	SYM
ejpam-5611	157	5	1	1	NUM
ejpam-5611	157	6	,	,	PUNCT
ejpam-5611	157	7	2	2	NUM
ejpam-5611	157	8	,	,	PUNCT
ejpam-5611	157	9	·	·	PUNCT
ejpam-5611	157	10	·	·	PUNCT
ejpam-5611	157	11	·	·	PUNCT
ejpam-5611	157	12	,	,	PUNCT
ejpam-5611	157	13	r.	r.	PROPN
ejpam-5611	157	14	thus	thus	ADV
ejpam-5611	157	15	,	,	PUNCT
ejpam-5611	157	16	supp	supp	NOUN
ejpam-5611	157	17	σk	σk	ADJ
ejpam-5611	157	18	·	·	PUNCT
ejpam-5611	157	19	χ[a	χ[a	PROPN
ejpam-5611	157	20	,	,	PUNCT
ejpam-5611	157	21	b	b	NOUN
ejpam-5611	157	22	]	]	X
ejpam-5611	157	23	⊆	⊆	NUM
ejpam-5611	157	24	b	b	PROPN
ejpam-5611	157	25	(	(	PUNCT
ejpam-5611	157	26	σk(ψ(y	σk(ψ(y	NOUN
ejpam-5611	157	27	)	)	PUNCT
ejpam-5611	157	28	)	)	PUNCT
ejpam-5611	157	29	,	,	PUNCT
ejpam-5611	157	30	δ0(ψ(y	δ0(ψ(y	NOUN
ejpam-5611	157	31	)	)	PUNCT
ejpam-5611	157	32	)	)	PUNCT
ejpam-5611	157	33	2	2	NUM
ejpam-5611	157	34	√	√	PROPN
ejpam-5611	157	35	p	p	NOUN
ejpam-5611	157	36	)	)	PUNCT
ejpam-5611	157	37	∩	∩	NOUN
ejpam-5611	157	38	[	[	X
ejpam-5611	157	39	a	a	DET
ejpam-5611	157	40	,	,	PUNCT
ejpam-5611	157	41	b	b	NOUN
ejpam-5611	157	42	]	]	X
ejpam-5611	157	43	⊆	⊆	NUM
ejpam-5611	157	44	jk	jk	PROPN
ejpam-5611	157	45	⊆	⊆	NUM
ejpam-5611	157	46	b	b	PROPN
ejpam-5611	157	47	(	(	PUNCT
ejpam-5611	157	48	σk(ψ(y	σk(ψ(y	NOUN
ejpam-5611	157	49	)	)	PUNCT
ejpam-5611	157	50	)	)	PUNCT
ejpam-5611	157	51	,	,	PUNCT
ejpam-5611	157	52	δ0(ψ(y	δ0(ψ(y	NOUN
ejpam-5611	157	53	)	)	PUNCT
ejpam-5611	157	54	)	)	PUNCT
ejpam-5611	157	55	)	)	PUNCT
ejpam-5611	157	56	∩	∩	NOUN
ejpam-5611	157	57	[	[	X
ejpam-5611	157	58	a	a	X
ejpam-5611	157	59	,	,	PUNCT
ejpam-5611	157	60	b	b	NOUN
ejpam-5611	157	61	]	]	X
ejpam-5611	157	62	,	,	PUNCT
ejpam-5611	157	63	that	that	ADV
ejpam-5611	157	64	is	is	ADV
ejpam-5611	157	65	,	,	PUNCT
ejpam-5611	157	66	supp	supp	ADJ
ejpam-5611	157	67	σk	σk	ADJ
ejpam-5611	157	68	·	·	PUNCT
ejpam-5611	157	69	χ[a	χ[a	PROPN
ejpam-5611	157	70	,	,	PUNCT
ejpam-5611	157	71	b	b	NOUN
ejpam-5611	157	72	]	]	PUNCT
ejpam-5611	157	73	⊆	⊆	NUM
ejpam-5611	157	74	jk	jk	PROPN
ejpam-5611	157	75	⊆	⊆	NUM
ejpam-5611	157	76	b	b	PROPN
ejpam-5611	157	77	(	(	PUNCT
ejpam-5611	157	78	σk(ψ(y	σk(ψ(y	NOUN
ejpam-5611	157	79	)	)	PUNCT
ejpam-5611	157	80	)	)	PUNCT
ejpam-5611	157	81	,	,	PUNCT
ejpam-5611	157	82	δ0(ψ(y	δ0(ψ(y	NOUN
ejpam-5611	157	83	)	)	PUNCT
ejpam-5611	157	84	)	)	PUNCT
ejpam-5611	157	85	)	)	PUNCT
ejpam-5611	157	86	∩	∩	NOUN
ejpam-5611	157	87	[	[	X
ejpam-5611	157	88	a	a	X
ejpam-5611	157	89	,	,	PUNCT
ejpam-5611	157	90	b	b	NOUN
ejpam-5611	157	91	]	]	X
ejpam-5611	157	92	(	(	PUNCT
ejpam-5611	157	93	3.8	3.8	NUM
ejpam-5611	157	94	)	)	PUNCT
ejpam-5611	157	95	for	for	ADP
ejpam-5611	157	96	all	all	PRON
ejpam-5611	157	97	k	k	NOUN
ejpam-5611	157	98	=	=	SYM
ejpam-5611	157	99	1	1	NUM
ejpam-5611	157	100	,	,	PUNCT
ejpam-5611	157	101	2	2	NUM
ejpam-5611	157	102	,	,	PUNCT
ejpam-5611	157	103	·	·	PUNCT
ejpam-5611	157	104	·	·	PUNCT
ejpam-5611	157	105	·	·	PUNCT
ejpam-5611	157	106	,	,	PUNCT
ejpam-5611	157	107	r.	r.	PROPN
ejpam-5611	157	108	note	note	VERB
ejpam-5611	157	109	that	that	SCONJ
ejpam-5611	157	110	on	on	ADP
ejpam-5611	157	111	[	[	X
ejpam-5611	157	112	a	a	X
ejpam-5611	157	113	,	,	PUNCT
ejpam-5611	157	114	b	b	NOUN
ejpam-5611	157	115	]	]	X
ejpam-5611	157	116	,	,	PUNCT
ejpam-5611	157	117	χ[a	χ[a	PROPN
ejpam-5611	157	118	,	,	PUNCT
ejpam-5611	157	119	b	b	NOUN
ejpam-5611	157	120	]	]	X
ejpam-5611	157	121	=	=	SYM
ejpam-5611	157	122	1	1	X
ejpam-5611	157	123	.	.	PUNCT
ejpam-5611	157	124	since	since	SCONJ
ejpam-5611	157	125	φk	φk	ADV
ejpam-5611	157	126	and	and	CCONJ
ejpam-5611	157	127	ψ−1	ψ−1	PROPN
ejpam-5611	157	128	are	be	AUX
ejpam-5611	157	129	continuously	continuously	ADV
ejpam-5611	157	130	differentiable	differentiable	ADJ
ejpam-5611	157	131	functions	function	NOUN
ejpam-5611	157	132	on	on	ADP
ejpam-5611	157	133	[	[	X
ejpam-5611	157	134	a	a	X
ejpam-5611	157	135	,	,	PUNCT
ejpam-5611	157	136	b	b	NOUN
ejpam-5611	157	137	]	]	X
ejpam-5611	157	138	,	,	PUNCT
ejpam-5611	157	139	σk	σk	X
ejpam-5611	157	140	·	·	PUNCT
ejpam-5611	157	141	χ[a	χ[a	PROPN
ejpam-5611	157	142	,	,	PUNCT
ejpam-5611	157	143	b	b	NOUN
ejpam-5611	157	144	]	]	X
ejpam-5611	157	145	=	=	PUNCT
ejpam-5611	157	146	σk	σk	PROPN
ejpam-5611	157	147	=	=	PUNCT
ejpam-5611	157	148	φk	φk	ADP
ejpam-5611	157	149	◦	◦	NOUN
ejpam-5611	157	150	ψ−1	ψ−1	PROPN
ejpam-5611	157	151	is	be	AUX
ejpam-5611	157	152	also	also	ADV
ejpam-5611	157	153	continuously	continuously	ADV
ejpam-5611	157	154	differentiable	differentiable	ADJ
ejpam-5611	157	155	function	function	NOUN
ejpam-5611	157	156	on	on	ADP
ejpam-5611	157	157	[	[	X
ejpam-5611	157	158	a	a	X
ejpam-5611	157	159	,	,	PUNCT
ejpam-5611	157	160	b	b	NOUN
ejpam-5611	157	161	]	]	PUNCT
ejpam-5611	157	162	.	.	PUNCT
ejpam-5611	158	1	fix	fix	NOUN
ejpam-5611	158	2	x	x	X
ejpam-5611	158	3	∈	∈	PROPN
ejpam-5611	159	1	[	[	X
ejpam-5611	159	2	a	a	X
ejpam-5611	159	3	,	,	PUNCT
ejpam-5611	159	4	b	b	NOUN
ejpam-5611	159	5	]	]	X
ejpam-5611	159	6	.	.	PUNCT
ejpam-5611	160	1	since	since	SCONJ
ejpam-5611	160	2	φk	φk	ADV
ejpam-5611	160	3	is	be	AUX
ejpam-5611	160	4	a	a	DET
ejpam-5611	160	5	partition	partition	NOUN
ejpam-5611	160	6	of	of	ADP
ejpam-5611	160	7	unity	unity	NOUN
ejpam-5611	160	8	for	for	ADP
ejpam-5611	160	9	all	all	PRON
ejpam-5611	160	10	k	k	NOUN
ejpam-5611	160	11	=	=	SYM
ejpam-5611	160	12	1	1	NUM
ejpam-5611	160	13	,	,	PUNCT
ejpam-5611	160	14	2	2	NUM
ejpam-5611	160	15	,	,	PUNCT
ejpam-5611	160	16	·	·	PUNCT
ejpam-5611	160	17	·	·	PUNCT
ejpam-5611	160	18	·	·	PUNCT
ejpam-5611	160	19	,	,	PUNCT
ejpam-5611	160	20	r	r	X
ejpam-5611	160	21	,	,	PUNCT
ejpam-5611	160	22	we	we	PRON
ejpam-5611	160	23	have	have	VERB
ejpam-5611	160	24	r∑	r∑	NOUN
ejpam-5611	160	25	k=1	k=1	X
ejpam-5611	160	26	σk	σk	X
ejpam-5611	160	27	·	·	SYM
ejpam-5611	160	28	χ[a	χ[a	ADJ
ejpam-5611	160	29	,	,	PUNCT
ejpam-5611	160	30	b](x	b](x	X
ejpam-5611	160	31	)	)	PUNCT
ejpam-5611	161	1	=	=	PUNCT
ejpam-5611	161	2	r∑	r∑	NOUN
ejpam-5611	161	3	k=1	k=1	X
ejpam-5611	161	4	σk(x	σk(x	PUNCT
ejpam-5611	161	5	)	)	PUNCT
ejpam-5611	161	6	=	=	SYM
ejpam-5611	162	1	r∑	r∑	NOUN
ejpam-5611	162	2	k=1	k=1	X
ejpam-5611	162	3	(	(	PUNCT
ejpam-5611	162	4	φk(ψ	φk(ψ	X
ejpam-5611	162	5	−1(x	−1(x	NOUN
ejpam-5611	162	6	)	)	PUNCT
ejpam-5611	162	7	)	)	PUNCT
ejpam-5611	163	1	=	=	SYM
ejpam-5611	163	2	1	1	X
ejpam-5611	163	3	.	.	PUNCT
ejpam-5611	163	4	g.	g.	PROPN
ejpam-5611	163	5	flores	flores	PROPN
ejpam-5611	163	6	,	,	PUNCT
ejpam-5611	163	7	a.	a.	PROPN
ejpam-5611	163	8	flores	flores	PROPN
ejpam-5611	163	9	/	/	SYM
ejpam-5611	163	10	eur	eur	PROPN
ejpam-5611	163	11	.	.	PUNCT
ejpam-5611	164	1	j.	j.	PROPN
ejpam-5611	164	2	pure	pure	PROPN
ejpam-5611	164	3	appl	appl	PROPN
ejpam-5611	164	4	.	.	PROPN
ejpam-5611	164	5	math	math	PROPN
ejpam-5611	164	6	,	,	PUNCT
ejpam-5611	164	7	18	18	NUM
ejpam-5611	164	8	(	(	PUNCT
ejpam-5611	164	9	2	2	NUM
ejpam-5611	164	10	)	)	PUNCT
ejpam-5611	164	11	(	(	PUNCT
ejpam-5611	164	12	2025	2025	NUM
ejpam-5611	164	13	)	)	PUNCT
ejpam-5611	164	14	,	,	PUNCT
ejpam-5611	164	15	5611	5611	NUM
ejpam-5611	164	16	8	8	NUM
ejpam-5611	164	17	of	of	ADP
ejpam-5611	164	18	16	16	NUM
ejpam-5611	164	19	this	this	PRON
ejpam-5611	164	20	means	mean	VERB
ejpam-5611	164	21	that	that	SCONJ
ejpam-5611	164	22	{	{	PUNCT
ejpam-5611	164	23	σk	σk	PROPN
ejpam-5611	164	24	·	·	PUNCT
ejpam-5611	164	25	χ−1	χ−1	ADJ
ejpam-5611	164	26	}	}	PUNCT
ejpam-5611	164	27	is	be	AUX
ejpam-5611	164	28	a	a	DET
ejpam-5611	164	29	partition	partition	NOUN
ejpam-5611	164	30	of	of	ADP
ejpam-5611	164	31	unity	unity	NOUN
ejpam-5611	164	32	on	on	ADP
ejpam-5611	164	33	[	[	X
ejpam-5611	164	34	a	a	X
ejpam-5611	164	35	,	,	PUNCT
ejpam-5611	164	36	b	b	NOUN
ejpam-5611	164	37	]	]	X
ejpam-5611	164	38	.	.	PUNCT
ejpam-5611	165	1	the	the	DET
ejpam-5611	165	2	inclusion	inclusion	NOUN
ejpam-5611	165	3	(	(	PUNCT
ejpam-5611	165	4	3.8	3.8	NUM
ejpam-5611	165	5	)	)	PUNCT
ejpam-5611	165	6	implies	imply	VERB
ejpam-5611	165	7	that	that	SCONJ
ejpam-5611	165	8	d0	d0	NOUN
ejpam-5611	165	9	=	=	SYM
ejpam-5611	165	10	{	{	PUNCT
ejpam-5611	165	11	(	(	PUNCT
ejpam-5611	165	12	xk	xk	PROPN
ejpam-5611	165	13	,	,	PUNCT
ejpam-5611	165	14	jk	jk	PROPN
ejpam-5611	165	15	,	,	PUNCT
ejpam-5611	165	16	σk	σk	ADV
ejpam-5611	165	17	·	·	PUNCT
ejpam-5611	165	18	χ−1)}rk=1	χ−1)}rk=1	NOUN
ejpam-5611	165	19	is	be	AUX
ejpam-5611	165	20	a	a	DET
ejpam-5611	165	21	δ0	δ0	NOUN
ejpam-5611	165	22	-	-	PUNCT
ejpam-5611	165	23	fine	fine	ADJ
ejpam-5611	165	24	division	division	NOUN
ejpam-5611	165	25	of	of	ADP
ejpam-5611	165	26	[	[	X
ejpam-5611	165	27	a	a	X
ejpam-5611	165	28	,	,	PUNCT
ejpam-5611	165	29	b	b	NOUN
ejpam-5611	165	30	]	]	X
ejpam-5611	165	31	.	.	PUNCT
ejpam-5611	166	1	next	next	ADV
ejpam-5611	166	2	,	,	PUNCT
ejpam-5611	166	3	we	we	PRON
ejpam-5611	166	4	will	will	AUX
ejpam-5611	166	5	show	show	VERB
ejpam-5611	166	6	that	that	SCONJ
ejpam-5611	166	7	for	for	ADP
ejpam-5611	166	8	each	each	PRON
ejpam-5611	166	9	k	k	NOUN
ejpam-5611	166	10	=	=	SYM
ejpam-5611	166	11	1	1	NUM
ejpam-5611	166	12	,	,	PUNCT
ejpam-5611	166	13	2	2	NUM
ejpam-5611	166	14	,	,	PUNCT
ejpam-5611	166	15	·	·	PUNCT
ejpam-5611	166	16	·	·	PUNCT
ejpam-5611	166	17	·	·	PUNCT
ejpam-5611	166	18	,	,	PUNCT
ejpam-5611	166	19	r	r	X
ejpam-5611	166	20	,	,	PUNCT
ejpam-5611	166	21	supp	supp	NOUN
ejpam-5611	166	22	σk	σk	ADP
ejpam-5611	166	23	◦	◦	NOUN
ejpam-5611	166	24	ψ	ψ	X
ejpam-5611	166	25	=	=	SYM
ejpam-5611	166	26	supp	supp	PROPN
ejpam-5611	166	27	φk	φk	PROPN
ejpam-5611	166	28	.	.	PROPN
ejpam-5611	166	29	indeed	indeed	ADV
ejpam-5611	166	30	,	,	PUNCT
ejpam-5611	166	31	let	let	VERB
ejpam-5611	166	32	k	k	PROPN
ejpam-5611	166	33	∈	∈	PROPN
ejpam-5611	166	34	{	{	PUNCT
ejpam-5611	166	35	1	1	NUM
ejpam-5611	166	36	,	,	PUNCT
ejpam-5611	166	37	2	2	NUM
ejpam-5611	166	38	,	,	PUNCT
ejpam-5611	166	39	·	·	PUNCT
ejpam-5611	166	40	·	·	PUNCT
ejpam-5611	166	41	·	·	PUNCT
ejpam-5611	166	42	,	,	PUNCT
ejpam-5611	166	43	r	r	X
ejpam-5611	166	44	}	}	PUNCT
ejpam-5611	166	45	and	and	CCONJ
ejpam-5611	166	46	let	let	VERB
ejpam-5611	166	47	x	x	X
ejpam-5611	166	48	∈	∈	PROPN
ejpam-5611	166	49	supp	supp	NOUN
ejpam-5611	167	1	σk	σk	ADP
ejpam-5611	167	2	◦	◦	NOUN
ejpam-5611	167	3	ψ	ψ	NOUN
ejpam-5611	167	4	.	.	PUNCT
ejpam-5611	167	5	then	then	ADV
ejpam-5611	167	6	σk(ψ(x	σk(ψ(x	ADV
ejpam-5611	167	7	)	)	PUNCT
ejpam-5611	167	8	)	)	PUNCT
ejpam-5611	167	9	>	>	X
ejpam-5611	167	10	0	0	PUNCT
ejpam-5611	168	1	and	and	CCONJ
ejpam-5611	168	2	so	so	ADV
ejpam-5611	168	3	ψ(x	ψ(x	NOUN
ejpam-5611	168	4	)	)	PUNCT
ejpam-5611	168	5	∈	∈	PROPN
ejpam-5611	168	6	supp	supp	NOUN
ejpam-5611	168	7	σk	σk	PROPN
ejpam-5611	168	8	=	=	PROPN
ejpam-5611	168	9	supp	supp	PROPN
ejpam-5611	168	10	φk	φk	ADP
ejpam-5611	168	11	◦	◦	NOUN
ejpam-5611	168	12	ψ−1	ψ−1	PROPN
ejpam-5611	168	13	.	.	PUNCT
ejpam-5611	169	1	hence	hence	ADV
ejpam-5611	169	2	,	,	PUNCT
ejpam-5611	169	3	x	x	PROPN
ejpam-5611	169	4	∈	∈	PROPN
ejpam-5611	169	5	supp	supp	NOUN
ejpam-5611	169	6	φk	φk	ADP
ejpam-5611	169	7	and	and	CCONJ
ejpam-5611	169	8	supp	supp	VERB
ejpam-5611	169	9	σk	σk	ADP
ejpam-5611	169	10	◦	◦	NOUN
ejpam-5611	169	11	ψ	ψ	NOUN
ejpam-5611	169	12	⊆	⊆	NUM
ejpam-5611	169	13	supp	supp	NOUN
ejpam-5611	169	14	φk	φk	ADP
ejpam-5611	169	15	.	.	PUNCT
ejpam-5611	170	1	now	now	ADV
ejpam-5611	170	2	,	,	PUNCT
ejpam-5611	170	3	let	let	VERB
ejpam-5611	170	4	k	k	PROPN
ejpam-5611	170	5	∈	∈	PROPN
ejpam-5611	170	6	{	{	PUNCT
ejpam-5611	170	7	1	1	NUM
ejpam-5611	170	8	,	,	PUNCT
ejpam-5611	170	9	2	2	NUM
ejpam-5611	170	10	,	,	PUNCT
ejpam-5611	170	11	·	·	PUNCT
ejpam-5611	170	12	·	·	PUNCT
ejpam-5611	170	13	·	·	PUNCT
ejpam-5611	170	14	,	,	PUNCT
ejpam-5611	170	15	r	r	NOUN
ejpam-5611	170	16	}	}	PUNCT
ejpam-5611	170	17	and	and	CCONJ
ejpam-5611	170	18	x	x	PUNCT
ejpam-5611	170	19	∈	∈	PROPN
ejpam-5611	170	20	supp	supp	PROPN
ejpam-5611	170	21	φk	φk	ADP
ejpam-5611	170	22	.	.	PROPN
ejpam-5611	171	1	then	then	ADV
ejpam-5611	171	2	φk(ψ	φk(ψ	NUM
ejpam-5611	171	3	−1(ψ(x	−1(ψ(x	NOUN
ejpam-5611	171	4	)	)	PUNCT
ejpam-5611	171	5	)	)	PUNCT
ejpam-5611	171	6	)	)	PUNCT
ejpam-5611	172	1	=	=	SYM
ejpam-5611	172	2	φk(x	φk(x	NOUN
ejpam-5611	172	3	)	)	PUNCT
ejpam-5611	172	4	>	>	X
ejpam-5611	172	5	0	0	NUM
ejpam-5611	172	6	;	;	PUNCT
ejpam-5611	172	7	and	and	CCONJ
ejpam-5611	172	8	so	so	ADV
ejpam-5611	172	9	ψ(x	ψ(x	NOUN
ejpam-5611	172	10	)	)	PUNCT
ejpam-5611	172	11	∈	∈	PROPN
ejpam-5611	172	12	supp	supp	NOUN
ejpam-5611	172	13	φk	φk	AUX
ejpam-5611	172	14	◦	◦	VERB
ejpam-5611	172	15	ψ−1	ψ−1	PROPN
ejpam-5611	172	16	=	=	SYM
ejpam-5611	172	17	supp	supp	NOUN
ejpam-5611	172	18	σk	σk	ADV
ejpam-5611	172	19	and	and	CCONJ
ejpam-5611	172	20	σk(ψ(x	σk(ψ(x	ADV
ejpam-5611	172	21	)	)	PUNCT
ejpam-5611	172	22	)	)	PUNCT
ejpam-5611	173	1	=	=	SYM
ejpam-5611	173	2	(	(	PUNCT
ejpam-5611	173	3	σk	σk	ADP
ejpam-5611	173	4	◦	◦	NOUN
ejpam-5611	173	5	ψ)(x	ψ)(x	PROPN
ejpam-5611	173	6	)	)	PUNCT
ejpam-5611	173	7	>	>	X
ejpam-5611	174	1	0	0	X
ejpam-5611	174	2	.	.	PUNCT
ejpam-5611	175	1	henceforth	henceforth	ADV
ejpam-5611	175	2	,	,	PUNCT
ejpam-5611	175	3	x	x	PROPN
ejpam-5611	175	4	∈	∈	NOUN
ejpam-5611	175	5	supp	supp	NOUN
ejpam-5611	175	6	σk	σk	ADP
ejpam-5611	175	7	◦	◦	NOUN
ejpam-5611	175	8	ψ	ψ	X
ejpam-5611	175	9	and	and	CCONJ
ejpam-5611	175	10	supp	supp	NOUN
ejpam-5611	175	11	φk	φk	ADP
ejpam-5611	175	12	⊆	⊆	NUM
ejpam-5611	175	13	supp	supp	NOUN
ejpam-5611	175	14	σk	σk	ADP
ejpam-5611	175	15	◦	◦	NOUN
ejpam-5611	175	16	ψ	ψ	NOUN
ejpam-5611	175	17	.	.	PUNCT
ejpam-5611	176	1	thus	thus	ADV
ejpam-5611	176	2	,	,	PUNCT
ejpam-5611	176	3	supp	supp	NOUN
ejpam-5611	176	4	φk	φk	ADP
ejpam-5611	176	5	=	=	SYM
ejpam-5611	176	6	supp	supp	PROPN
ejpam-5611	176	7	σk	σk	ADP
ejpam-5611	176	8	◦	◦	NOUN
ejpam-5611	176	9	ψ	ψ	NOUN
ejpam-5611	176	10	.	.	PUNCT
ejpam-5611	177	1	by	by	ADP
ejpam-5611	177	2	lemma	lemma	PROPN
ejpam-5611	177	3	1,∫	1,∫	PROPN
ejpam-5611	177	4	jk	jk	PROPN
ejpam-5611	177	5	σk	σk	PROPN
ejpam-5611	177	6	=	=	PROPN
ejpam-5611	177	7	∫	∫	PROPN
ejpam-5611	177	8	ψ−1(jk	ψ−1(jk	PROPN
ejpam-5611	177	9	)	)	PUNCT
ejpam-5611	177	10	(	(	PUNCT
ejpam-5611	177	11	σk	σk	AUX
ejpam-5611	177	12	◦	◦	VERB
ejpam-5611	177	13	ψ)|detψ|	ψ)|detψ|	PROPN
ejpam-5611	177	14	=	=	SYM
ejpam-5611	177	15	∫	∫	PROPN
ejpam-5611	177	16	ik	ik	PROPN
ejpam-5611	177	17	φk|	φk|	PROPN
ejpam-5611	177	18	detψ|	detψ|	PROPN
ejpam-5611	177	19	.	.	PUNCT
ejpam-5611	178	1	notice	notice	PROPN
ejpam-5611	179	1	that∥∥∥∥	that∥∥∥∥	PROPN
ejpam-5611	179	2	s∑	s∑	PROPN
ejpam-5611	179	3	k=1	k=1	PROPN
ejpam-5611	179	4	f(ψ(ξk))|detψ|χψ−1([a	f(ψ(ξk))|detψ|χψ−1([a	PROPN
ejpam-5611	179	5	,	,	PUNCT
ejpam-5611	179	6	b])(ξk	b])(ξk	PROPN
ejpam-5611	179	7	)	)	PUNCT
ejpam-5611	179	8	∫	∫	PROPN
ejpam-5611	179	9	ik	ik	PROPN
ejpam-5611	179	10	φk	φk	ADP
ejpam-5611	179	11	−	−	PROPN
ejpam-5611	179	12	p∑	p∑	X
ejpam-5611	179	13	k=1	k=1	X
ejpam-5611	179	14	f(xk	f(xk	X
ejpam-5611	179	15	)	)	PUNCT
ejpam-5611	179	16	∫	∫	PROPN
ejpam-5611	179	17	jk	jk	PROPN
ejpam-5611	179	18	σkχ[a	σkχ[a	PROPN
ejpam-5611	179	19	,	,	PUNCT
ejpam-5611	179	20	b	b	NOUN
ejpam-5611	179	21	]	]	PUNCT
ejpam-5611	179	22	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-5611	179	23	=	=	SYM
ejpam-5611	179	24	∥∥∥∥	∥∥∥∥	NUM
ejpam-5611	179	25	p∑	p∑	X
ejpam-5611	180	1	k=1	k=1	PROPN
ejpam-5611	180	2	f(ψ(ξk))|detψ|	f(ψ(ξk))|detψ|	PROPN
ejpam-5611	180	3	∫	∫	PROPN
ejpam-5611	180	4	ik	ik	PROPN
ejpam-5611	180	5	φk	φk	ADP
ejpam-5611	180	6	−	−	PROPN
ejpam-5611	180	7	p∑	p∑	X
ejpam-5611	180	8	k=1	k=1	X
ejpam-5611	180	9	f(xk	f(xk	X
ejpam-5611	180	10	)	)	PUNCT
ejpam-5611	180	11	∫	∫	PROPN
ejpam-5611	180	12	jk	jk	PROPN
ejpam-5611	180	13	σk	σk	ADP
ejpam-5611	180	14	∥∥∥∥	∥∥∥∥	NUM
ejpam-5611	180	15	=	=	SYM
ejpam-5611	180	16	∥∥∥∥	∥∥∥∥	NUM
ejpam-5611	180	17	p∑	p∑	X
ejpam-5611	181	1	k=1	k=1	PROPN
ejpam-5611	181	2	f(ψ(ξk))|detψ|	f(ψ(ξk))|detψ|	PROPN
ejpam-5611	181	3	∫	∫	PROPN
ejpam-5611	181	4	ik	ik	PROPN
ejpam-5611	181	5	φk	φk	ADP
ejpam-5611	181	6	−	−	PROPN
ejpam-5611	181	7	p∑	p∑	X
ejpam-5611	182	1	k=1	k=1	PROPN
ejpam-5611	183	1	f(ψ(ξk))|detψ|	f(ψ(ξk))|detψ|	PROPN
ejpam-5611	183	2	∫	∫	PROPN
ejpam-5611	183	3	ik	ik	PROPN
ejpam-5611	183	4	φk	φk	ADP
ejpam-5611	183	5	∥∥∥∥	∥∥∥∥	NUM
ejpam-5611	183	6	=	=	SYM
ejpam-5611	183	7	0	0	NUM
ejpam-5611	183	8	implies	imply	VERB
ejpam-5611	183	9	s∑	s∑	PROPN
ejpam-5611	183	10	k=1	k=1	PROPN
ejpam-5611	183	11	f(ψ(ξk))|	f(ψ(ξk))|	PROPN
ejpam-5611	183	12	detψ|χψ−1(e)(ξk	detψ|χψ−1(e)(ξk	PROPN
ejpam-5611	183	13	)	)	PUNCT
ejpam-5611	183	14	∫	∫	PROPN
ejpam-5611	183	15	ik	ik	PROPN
ejpam-5611	183	16	φk	φk	ADP
ejpam-5611	183	17	=	=	SYM
ejpam-5611	183	18	p∑	p∑	X
ejpam-5611	183	19	k=1	k=1	PUNCT
ejpam-5611	183	20	f(xk	f(xk	X
ejpam-5611	183	21	)	)	PUNCT
ejpam-5611	183	22	∫	∫	PROPN
ejpam-5611	183	23	jk	jk	PROPN
ejpam-5611	183	24	σkχe	σkχe	PROPN
ejpam-5611	183	25	.	.	PUNCT
ejpam-5611	184	1	(	(	PUNCT
ejpam-5611	184	2	3.9	3.9	NUM
ejpam-5611	184	3	)	)	PUNCT
ejpam-5611	184	4	since	since	SCONJ
ejpam-5611	184	5	d0	d0	NOUN
ejpam-5611	184	6	is	be	AUX
ejpam-5611	184	7	a	a	DET
ejpam-5611	184	8	δ0	δ0	NOUN
ejpam-5611	184	9	-	-	PUNCT
ejpam-5611	184	10	fine	fine	ADJ
ejpam-5611	184	11	division	division	NOUN
ejpam-5611	184	12	of	of	ADP
ejpam-5611	184	13	[	[	X
ejpam-5611	184	14	a	a	X
ejpam-5611	184	15	,	,	PUNCT
ejpam-5611	184	16	b],∥∥∥∥	b],∥∥∥∥	PROPN
ejpam-5611	184	17	p∑	p∑	NOUN
ejpam-5611	185	1	k=1	k=1	X
ejpam-5611	185	2	f(xk	f(xk	X
ejpam-5611	185	3	)	)	PUNCT
ejpam-5611	185	4	∫	∫	PROPN
ejpam-5611	185	5	jk	jk	PROPN
ejpam-5611	185	6	σkχe	σkχe	PROPN
ejpam-5611	185	7	−	−	PROPN
ejpam-5611	185	8	(	(	PUNCT
ejpam-5611	185	9	p	p	NOUN
ejpam-5611	185	10	)	)	PUNCT
ejpam-5611	185	11	∫	∫	PROPN
ejpam-5611	186	1	[	[	X
ejpam-5611	186	2	a	a	X
ejpam-5611	186	3	,	,	PUNCT
ejpam-5611	186	4	b	b	NOUN
ejpam-5611	186	5	]	]	X
ejpam-5611	186	6	f	f	X
ejpam-5611	186	7	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5611	186	8	<	<	X
ejpam-5611	186	9	ϵ	ϵ	X
ejpam-5611	186	10	;	;	PUNCT
ejpam-5611	186	11	that	that	PRON
ejpam-5611	186	12	is	be	AUX
ejpam-5611	186	13	,	,	PUNCT
ejpam-5611	186	14	∥∥∥∥	∥∥∥∥	NUM
ejpam-5611	186	15	s∑	s∑	PROPN
ejpam-5611	186	16	k=1	k=1	PROPN
ejpam-5611	186	17	f(ψ(ξk))|detψ|χψ−1(e)(ξk	f(ψ(ξk))|detψ|χψ−1(e)(ξk	PROPN
ejpam-5611	186	18	)	)	PUNCT
ejpam-5611	186	19	∫	∫	PROPN
ejpam-5611	186	20	ik	ik	PROPN
ejpam-5611	186	21	φk	φk	ADP
ejpam-5611	186	22	−	−	PROPN
ejpam-5611	186	23	(	(	PUNCT
ejpam-5611	186	24	p	p	NOUN
ejpam-5611	186	25	)	)	PUNCT
ejpam-5611	186	26	∫	∫	PROPN
ejpam-5611	187	1	[	[	X
ejpam-5611	187	2	a	a	X
ejpam-5611	187	3	,	,	PUNCT
ejpam-5611	187	4	b	b	NOUN
ejpam-5611	187	5	]	]	X
ejpam-5611	187	6	f	f	X
ejpam-5611	187	7	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5611	187	8	<	<	X
ejpam-5611	187	9	ϵ	ϵ	X
ejpam-5611	187	10	this	this	PRON
ejpam-5611	187	11	simply	simply	ADV
ejpam-5611	187	12	means	mean	VERB
ejpam-5611	187	13	,	,	PUNCT
ejpam-5611	187	14	(	(	PUNCT
ejpam-5611	187	15	f	f	X
ejpam-5611	187	16	◦	◦	NOUN
ejpam-5611	187	17	ψ)χψ−1([a	ψ)χψ−1([a	PROPN
ejpam-5611	187	18	,	,	PUNCT
ejpam-5611	187	19	b	b	NOUN
ejpam-5611	187	20	]	]	X
ejpam-5611	187	21	)	)	PUNCT
ejpam-5611	187	22	is	be	AUX
ejpam-5611	187	23	pu	pu	PROPN
ejpam-5611	187	24	integrable	integrable	ADJ
ejpam-5611	187	25	with	with	ADP
ejpam-5611	187	26	over	over	ADP
ejpam-5611	187	27	e	e	NOUN
ejpam-5611	187	28	and	and	CCONJ
ejpam-5611	187	29	(	(	PUNCT
ejpam-5611	187	30	p	p	X
ejpam-5611	187	31	)	)	PUNCT
ejpam-5611	187	32	∫	∫	PROPN
ejpam-5611	188	1	[	[	X
ejpam-5611	188	2	a	a	X
ejpam-5611	188	3	,	,	PUNCT
ejpam-5611	188	4	b	b	NOUN
ejpam-5611	188	5	]	]	X
ejpam-5611	188	6	f	f	X
ejpam-5611	188	7	=	=	PUNCT
ejpam-5611	188	8	(	(	PUNCT
ejpam-5611	188	9	p	p	NOUN
ejpam-5611	188	10	)	)	PUNCT
ejpam-5611	188	11	∫	∫	PROPN
ejpam-5611	188	12	ψ−1([a	ψ−1([a	PROPN
ejpam-5611	188	13	,	,	PUNCT
ejpam-5611	188	14	b	b	NOUN
ejpam-5611	188	15	]	]	X
ejpam-5611	188	16	)	)	PUNCT
ejpam-5611	188	17	(	(	PUNCT
ejpam-5611	188	18	f	f	X
ejpam-5611	188	19	◦	◦	NOUN
ejpam-5611	188	20	ψ	ψ	SYM
ejpam-5611	188	21	)	)	PUNCT
ejpam-5611	188	22	dψ	dψ	NOUN
ejpam-5611	188	23	.	.	PUNCT
ejpam-5611	189	1	□	□	PUNCT
ejpam-5611	189	2	g.	g.	PROPN
ejpam-5611	189	3	flores	flores	PROPN
ejpam-5611	189	4	,	,	PUNCT
ejpam-5611	189	5	a.	a.	PROPN
ejpam-5611	189	6	flores	flores	PROPN
ejpam-5611	189	7	/	/	SYM
ejpam-5611	189	8	eur	eur	PROPN
ejpam-5611	189	9	.	.	PUNCT
ejpam-5611	190	1	j.	j.	PROPN
ejpam-5611	190	2	pure	pure	PROPN
ejpam-5611	190	3	appl	appl	PROPN
ejpam-5611	190	4	.	.	PROPN
ejpam-5611	190	5	math	math	PROPN
ejpam-5611	190	6	,	,	PUNCT
ejpam-5611	190	7	18	18	NUM
ejpam-5611	190	8	(	(	PUNCT
ejpam-5611	190	9	2	2	NUM
ejpam-5611	190	10	)	)	PUNCT
ejpam-5611	190	11	(	(	PUNCT
ejpam-5611	190	12	2025	2025	NUM
ejpam-5611	190	13	)	)	PUNCT
ejpam-5611	190	14	,	,	PUNCT
ejpam-5611	190	15	5611	5611	NUM
ejpam-5611	190	16	9	9	NUM
ejpam-5611	190	17	of	of	ADP
ejpam-5611	190	18	16	16	NUM
ejpam-5611	190	19	lemma	lemma	PROPN
ejpam-5611	190	20	2	2	NUM
ejpam-5611	190	21	.	.	PUNCT
ejpam-5611	191	1	let	let	VERB
ejpam-5611	191	2	dp	dp	NOUN
ejpam-5611	191	3	=	=	SYM
ejpam-5611	191	4	{	{	PUNCT
ejpam-5611	191	5	ξ	ξ	PROPN
ejpam-5611	191	6	,	,	PUNCT
ejpam-5611	191	7	i	i	PRON
ejpam-5611	191	8	,	,	PUNCT
ejpam-5611	191	9	φ	φ	PROPN
ejpam-5611	191	10	}	}	PUNCT
ejpam-5611	191	11	be	be	AUX
ejpam-5611	191	12	a	a	DET
ejpam-5611	191	13	partial	partial	ADJ
ejpam-5611	191	14	δ	δ	NOUN
ejpam-5611	191	15	-	-	PUNCT
ejpam-5611	191	16	fine	fine	ADJ
ejpam-5611	191	17	division	division	NOUN
ejpam-5611	191	18	of	of	ADP
ejpam-5611	191	19	[	[	X
ejpam-5611	191	20	a	a	X
ejpam-5611	191	21	,	,	PUNCT
ejpam-5611	191	22	b	b	NOUN
ejpam-5611	191	23	]	]	X
ejpam-5611	191	24	,	,	PUNCT
ejpam-5611	191	25	σ(x	σ(x	PROPN
ejpam-5611	191	26	)	)	PUNCT
ejpam-5611	191	27	=	=	PUNCT
ejpam-5611	191	28	∑	∑	PUNCT
ejpam-5611	191	29	d1	d1	PROPN
ejpam-5611	191	30	φ(x	φ(x	NOUN
ejpam-5611	191	31	)	)	PUNCT
ejpam-5611	191	32	,	,	PUNCT
ejpam-5611	191	33	and	and	CCONJ
ejpam-5611	191	34	df	df	PROPN
ejpam-5611	191	35	=	=	SYM
ejpam-5611	191	36	{	{	PUNCT
ejpam-5611	191	37	(	(	PUNCT
ejpam-5611	191	38	η	η	PROPN
ejpam-5611	191	39	,	,	PUNCT
ejpam-5611	191	40	j	j	PROPN
ejpam-5611	191	41	,	,	PUNCT
ejpam-5611	191	42	ψ	ψ	PROPN
ejpam-5611	191	43	)	)	PUNCT
ejpam-5611	191	44	}	}	PUNCT
ejpam-5611	191	45	be	be	VERB
ejpam-5611	191	46	δ	δ	PROPN
ejpam-5611	191	47	-	-	PUNCT
ejpam-5611	191	48	fine	fine	ADJ
ejpam-5611	191	49	division	division	NOUN
ejpam-5611	191	50	of	of	ADP
ejpam-5611	191	51	[	[	X
ejpam-5611	191	52	a	a	X
ejpam-5611	191	53	,	,	PUNCT
ejpam-5611	191	54	b	b	NOUN
ejpam-5611	191	55	]	]	X
ejpam-5611	191	56	.	.	PUNCT
ejpam-5611	192	1	then	then	ADV
ejpam-5611	192	2	dp	dp	NOUN
ejpam-5611	192	3	∪	∪	X
ejpam-5611	192	4	{	{	PUNCT
ejpam-5611	192	5	(	(	PUNCT
ejpam-5611	192	6	η	η	PROPN
ejpam-5611	192	7	,	,	PUNCT
ejpam-5611	192	8	j	j	PROPN
ejpam-5611	192	9	,	,	PUNCT
ejpam-5611	192	10	(	(	PUNCT
ejpam-5611	192	11	1−	1−	NUM
ejpam-5611	192	12	σ)ψ	σ)ψ	X
ejpam-5611	192	13	)	)	PUNCT
ejpam-5611	192	14	}	}	PUNCT
ejpam-5611	192	15	is	be	AUX
ejpam-5611	192	16	a	a	DET
ejpam-5611	192	17	δ	δ	NOUN
ejpam-5611	192	18	-	-	PUNCT
ejpam-5611	192	19	fine	fine	ADJ
ejpam-5611	192	20	division	division	NOUN
ejpam-5611	192	21	of	of	ADP
ejpam-5611	192	22	[	[	X
ejpam-5611	192	23	a	a	X
ejpam-5611	192	24	,	,	PUNCT
ejpam-5611	192	25	b	b	NOUN
ejpam-5611	192	26	]	]	PUNCT
ejpam-5611	192	27	.	.	PUNCT
ejpam-5611	193	1	proof	proof	NOUN
ejpam-5611	193	2	:	:	PUNCT
ejpam-5611	193	3	let	let	VERB
ejpam-5611	193	4	x	x	X
ejpam-5611	193	5	∈	∈	PROPN
ejpam-5611	193	6	[	[	X
ejpam-5611	193	7	a	a	X
ejpam-5611	193	8	,	,	PUNCT
ejpam-5611	193	9	b	b	NOUN
ejpam-5611	193	10	]	]	X
ejpam-5611	193	11	.	.	PUNCT
ejpam-5611	194	1	since	since	SCONJ
ejpam-5611	194	2	df	df	PROPN
ejpam-5611	194	3	is	be	AUX
ejpam-5611	194	4	a	a	DET
ejpam-5611	194	5	δ	δ	NOUN
ejpam-5611	194	6	-	-	PUNCT
ejpam-5611	194	7	fine	fine	ADJ
ejpam-5611	194	8	division	division	NOUN
ejpam-5611	194	9	of	of	ADP
ejpam-5611	194	10	[	[	X
ejpam-5611	194	11	a	a	X
ejpam-5611	194	12	,	,	PUNCT
ejpam-5611	194	13	b	b	NOUN
ejpam-5611	194	14	]	]	X
ejpam-5611	194	15	,	,	PUNCT
ejpam-5611	194	16	{	{	PUNCT
ejpam-5611	194	17	ψ	ψ	AUX
ejpam-5611	194	18	}	}	PUNCT
ejpam-5611	194	19	is	be	AUX
ejpam-5611	194	20	a	a	DET
ejpam-5611	194	21	partition	partition	NOUN
ejpam-5611	194	22	of	of	ADP
ejpam-5611	194	23	unity	unity	NOUN
ejpam-5611	194	24	.	.	PUNCT
ejpam-5611	195	1	thus	thus	ADV
ejpam-5611	195	2	,	,	PUNCT
ejpam-5611	195	3	∑	∑	PROPN
ejpam-5611	195	4	df	df	PROPN
ejpam-5611	195	5	ψ(x	ψ(x	PROPN
ejpam-5611	195	6	)	)	PUNCT
ejpam-5611	195	7	=	=	SYM
ejpam-5611	195	8	1	1	X
ejpam-5611	195	9	.	.	X
ejpam-5611	195	10	observe	observe	VERB
ejpam-5611	195	11	that∑	that∑	NOUN
ejpam-5611	195	12	dp	dp	NOUN
ejpam-5611	195	13	φ(x	φ(x	NOUN
ejpam-5611	195	14	)	)	PUNCT
ejpam-5611	196	1	+	+	CCONJ
ejpam-5611	196	2	∑	∑	PROPN
ejpam-5611	196	3	df	df	PROPN
ejpam-5611	196	4	(	(	PUNCT
ejpam-5611	196	5	1−	1−	NUM
ejpam-5611	196	6	σ(x	σ(x	NOUN
ejpam-5611	196	7	)	)	PUNCT
ejpam-5611	196	8	)	)	PUNCT
ejpam-5611	196	9	·	·	PUNCT
ejpam-5611	196	10	ψ(x	ψ(x	NUM
ejpam-5611	196	11	)	)	PUNCT
ejpam-5611	196	12	=	=	SYM
ejpam-5611	196	13	σ(x	σ(x	X
ejpam-5611	196	14	)	)	PUNCT
ejpam-5611	197	1	+	+	CCONJ
ejpam-5611	197	2	∑	∑	PROPN
ejpam-5611	197	3	df	df	PROPN
ejpam-5611	197	4	ψ(x)−	ψ(x)−	PROPN
ejpam-5611	197	5	σ(x	σ(x	PROPN
ejpam-5611	197	6	)	)	PUNCT
ejpam-5611	197	7	∑	∑	PROPN
ejpam-5611	197	8	df	df	PROPN
ejpam-5611	197	9	ψ(x	ψ(x	PROPN
ejpam-5611	197	10	)	)	PUNCT
ejpam-5611	197	11	=	=	SYM
ejpam-5611	197	12	σ(x	σ(x	X
ejpam-5611	197	13	)	)	PUNCT
ejpam-5611	197	14	+	+	CCONJ
ejpam-5611	197	15	1−	1−	NUM
ejpam-5611	197	16	σ(x	σ(x	NOUN
ejpam-5611	197	17	)	)	PUNCT
ejpam-5611	197	18	·	·	PUNCT
ejpam-5611	197	19	1	1	NUM
ejpam-5611	197	20	=	=	SYM
ejpam-5611	197	21	1	1	X
ejpam-5611	197	22	.	.	PUNCT
ejpam-5611	198	1	this	this	PRON
ejpam-5611	198	2	means	mean	VERB
ejpam-5611	198	3	that	that	SCONJ
ejpam-5611	198	4	{	{	PUNCT
ejpam-5611	198	5	φ	φ	NOUN
ejpam-5611	198	6	}	}	PUNCT
ejpam-5611	198	7	∪	∪	X
ejpam-5611	198	8	{	{	PUNCT
ejpam-5611	198	9	(	(	PUNCT
ejpam-5611	198	10	1	1	NUM
ejpam-5611	198	11	−	−	NOUN
ejpam-5611	198	12	σ)ψ	σ)ψ	X
ejpam-5611	198	13	}	}	PUNCT
ejpam-5611	198	14	is	be	AUX
ejpam-5611	198	15	a	a	DET
ejpam-5611	198	16	partition	partition	NOUN
ejpam-5611	198	17	of	of	ADP
ejpam-5611	198	18	unity	unity	NOUN
ejpam-5611	198	19	.	.	PUNCT
ejpam-5611	199	1	since	since	SCONJ
ejpam-5611	199	2	dp	dp	NOUN
ejpam-5611	199	3	is	be	AUX
ejpam-5611	199	4	a	a	DET
ejpam-5611	199	5	partial	partial	ADJ
ejpam-5611	199	6	δ	δ	NOUN
ejpam-5611	199	7	-	-	PUNCT
ejpam-5611	199	8	fine	fine	ADJ
ejpam-5611	199	9	division	division	NOUN
ejpam-5611	199	10	of	of	ADP
ejpam-5611	199	11	[	[	X
ejpam-5611	199	12	a	a	X
ejpam-5611	199	13	,	,	PUNCT
ejpam-5611	199	14	b	b	NOUN
ejpam-5611	199	15	]	]	X
ejpam-5611	199	16	,	,	PUNCT
ejpam-5611	199	17	it	it	PRON
ejpam-5611	199	18	follows	follow	VERB
ejpam-5611	199	19	that	that	SCONJ
ejpam-5611	199	20	supp	supp	PROPN
ejpam-5611	199	21	φ	φ	PROPN
ejpam-5611	199	22	⊆	⊆	NUM
ejpam-5611	199	23	i	i	PROPN
ejpam-5611	199	24	⊆	⊆	NUM
ejpam-5611	199	25	b(ξ	b(ξ	NOUN
ejpam-5611	199	26	,	,	PUNCT
ejpam-5611	199	27	δ(ξ	δ(ξ	NOUN
ejpam-5611	199	28	)	)	PUNCT
ejpam-5611	199	29	)	)	PUNCT
ejpam-5611	199	30	.	.	PUNCT
ejpam-5611	200	1	(	(	PUNCT
ejpam-5611	200	2	3.10	3.10	NUM
ejpam-5611	200	3	)	)	PUNCT
ejpam-5611	200	4	now	now	ADV
ejpam-5611	200	5	,	,	PUNCT
ejpam-5611	200	6	let	let	VERB
ejpam-5611	200	7	x	x	X
ejpam-5611	200	8	∈	∈	PROPN
ejpam-5611	200	9	supp	supp	NOUN
ejpam-5611	200	10	(	(	PUNCT
ejpam-5611	200	11	(	(	PUNCT
ejpam-5611	200	12	1	1	NUM
ejpam-5611	200	13	−	−	PROPN
ejpam-5611	200	14	σ	σ	PROPN
ejpam-5611	200	15	)	)	PUNCT
ejpam-5611	200	16	·	·	PUNCT
ejpam-5611	201	1	ψ	ψ	X
ejpam-5611	201	2	)	)	PUNCT
ejpam-5611	201	3	.	.	PUNCT
ejpam-5611	202	1	then	then	ADV
ejpam-5611	202	2	(	(	PUNCT
ejpam-5611	202	3	1	1	NUM
ejpam-5611	202	4	−	−	PROPN
ejpam-5611	202	5	σ(x	σ(x	NOUN
ejpam-5611	202	6	)	)	PUNCT
ejpam-5611	202	7	)	)	PUNCT
ejpam-5611	203	1	·	·	PUNCT
ejpam-5611	203	2	ψ(x	ψ(x	NOUN
ejpam-5611	203	3	)	)	PUNCT
ejpam-5611	203	4	>	>	X
ejpam-5611	203	5	0	0	PUNCT
ejpam-5611	204	1	and	and	CCONJ
ejpam-5611	204	2	so	so	ADV
ejpam-5611	204	3	ψ(x	ψ(x	NUM
ejpam-5611	204	4	)	)	PUNCT
ejpam-5611	204	5	>	>	X
ejpam-5611	205	1	0	0	X
ejpam-5611	205	2	.	.	PUNCT
ejpam-5611	206	1	hence	hence	ADV
ejpam-5611	206	2	,	,	PUNCT
ejpam-5611	206	3	x	x	PUNCT
ejpam-5611	206	4	∈	∈	PROPN
ejpam-5611	206	5	supp	supp	PROPN
ejpam-5611	206	6	ψ	ψ	X
ejpam-5611	206	7	.	.	PUNCT
ejpam-5611	207	1	thus	thus	ADV
ejpam-5611	207	2	,	,	PUNCT
ejpam-5611	207	3	supp	supp	PROPN
ejpam-5611	207	4	(	(	PUNCT
ejpam-5611	207	5	(	(	PUNCT
ejpam-5611	207	6	1−	1−	NUM
ejpam-5611	207	7	φ	φ	NUM
ejpam-5611	207	8	)	)	PUNCT
ejpam-5611	207	9	·	·	PUNCT
ejpam-5611	207	10	ψ	ψ	X
ejpam-5611	207	11	)	)	PUNCT
ejpam-5611	207	12	⊆	⊆	NUM
ejpam-5611	207	13	supp	supp	PROPN
ejpam-5611	207	14	ψ	ψ	X
ejpam-5611	207	15	.	.	PUNCT
ejpam-5611	208	1	so	so	ADV
ejpam-5611	208	2	we	we	PRON
ejpam-5611	208	3	have	have	VERB
ejpam-5611	208	4	supp	supp	NOUN
ejpam-5611	208	5	(	(	PUNCT
ejpam-5611	208	6	(	(	PUNCT
ejpam-5611	208	7	1−	1−	NUM
ejpam-5611	208	8	σ	σ	NUM
ejpam-5611	208	9	)	)	PUNCT
ejpam-5611	208	10	·	·	PUNCT
ejpam-5611	209	1	ψ	ψ	X
ejpam-5611	209	2	)	)	PUNCT
ejpam-5611	209	3	⊆	⊆	NUM
ejpam-5611	209	4	supp	supp	NOUN
ejpam-5611	209	5	ψ	ψ	ADP
ejpam-5611	209	6	⊆	⊆	NUM
ejpam-5611	209	7	j	j	PROPN
ejpam-5611	209	8	⊆	⊆	NUM
ejpam-5611	209	9	b(η	b(η	NOUN
ejpam-5611	209	10	,	,	PUNCT
ejpam-5611	209	11	δ(η	δ(η	PROPN
ejpam-5611	209	12	)	)	PUNCT
ejpam-5611	209	13	)	)	PUNCT
ejpam-5611	209	14	.	.	PUNCT
ejpam-5611	210	1	(	(	PUNCT
ejpam-5611	210	2	3.11	3.11	NUM
ejpam-5611	210	3	)	)	PUNCT
ejpam-5611	210	4	by	by	ADP
ejpam-5611	210	5	the	the	DET
ejpam-5611	210	6	inclusions	inclusion	NOUN
ejpam-5611	210	7	in	in	ADP
ejpam-5611	210	8	3.10	3.10	NUM
ejpam-5611	210	9	and	and	CCONJ
ejpam-5611	210	10	3.11	3.11	NUM
ejpam-5611	210	11	,	,	PUNCT
ejpam-5611	210	12	evidently	evidently	ADV
ejpam-5611	210	13	d	d	X
ejpam-5611	210	14	∪	∪	X
ejpam-5611	210	15	{	{	PUNCT
ejpam-5611	210	16	(	(	PUNCT
ejpam-5611	210	17	η	η	PROPN
ejpam-5611	210	18	,	,	PUNCT
ejpam-5611	210	19	j	j	PROPN
ejpam-5611	210	20	,	,	PUNCT
ejpam-5611	210	21	(	(	PUNCT
ejpam-5611	210	22	1−	1−	NUM
ejpam-5611	210	23	σ)ψ	σ)ψ	X
ejpam-5611	210	24	)	)	PUNCT
ejpam-5611	210	25	}	}	PUNCT
ejpam-5611	210	26	is	be	AUX
ejpam-5611	210	27	a	a	DET
ejpam-5611	210	28	δ	δ	NOUN
ejpam-5611	210	29	-	-	PUNCT
ejpam-5611	210	30	fine	fine	ADJ
ejpam-5611	210	31	division	division	NOUN
ejpam-5611	210	32	of	of	ADP
ejpam-5611	210	33	[	[	X
ejpam-5611	210	34	a	a	X
ejpam-5611	210	35	,	,	PUNCT
ejpam-5611	210	36	b	b	NOUN
ejpam-5611	210	37	]	]	X
ejpam-5611	210	38	.	.	PUNCT
ejpam-5611	211	1	□	□	PUNCT
ejpam-5611	211	2	lemma	lemma	PROPN
ejpam-5611	211	3	3	3	X
ejpam-5611	211	4	.	.	PUNCT
ejpam-5611	212	1	let	let	VERB
ejpam-5611	212	2	f	f	NOUN
ejpam-5611	212	3	:	:	PUNCT
ejpam-5611	213	1	[	[	X
ejpam-5611	213	2	a	a	X
ejpam-5611	213	3	,	,	PUNCT
ejpam-5611	213	4	b	b	NOUN
ejpam-5611	213	5	]	]	X
ejpam-5611	213	6	→	→	PUNCT
ejpam-5611	213	7	x	x	X
ejpam-5611	213	8	be	be	AUX
ejpam-5611	213	9	a	a	DET
ejpam-5611	213	10	pu	pu	PROPN
ejpam-5611	213	11	integrable	integrable	ADJ
ejpam-5611	213	12	function	function	NOUN
ejpam-5611	213	13	over	over	ADP
ejpam-5611	213	14	[	[	X
ejpam-5611	213	15	a	a	PRON
ejpam-5611	213	16	,	,	PUNCT
ejpam-5611	213	17	b	b	NOUN
ejpam-5611	213	18	]	]	X
ejpam-5611	213	19	.	.	PUNCT
ejpam-5611	214	1	if	if	SCONJ
ejpam-5611	214	2	g	g	PROPN
ejpam-5611	214	3	be	be	VERB
ejpam-5611	214	4	an	an	DET
ejpam-5611	214	5	open	open	ADJ
ejpam-5611	214	6	and	and	CCONJ
ejpam-5611	214	7	bounded	bound	VERB
ejpam-5611	214	8	set	set	VERB
ejpam-5611	214	9	such	such	ADJ
ejpam-5611	214	10	that	that	DET
ejpam-5611	214	11	supp	supp	NOUN
ejpam-5611	214	12	f	f	PROPN
ejpam-5611	215	1	⊆	⊆	NUM
ejpam-5611	215	2	g	g	PROPN
ejpam-5611	215	3	⊆	⊆	NUM
ejpam-5611	215	4	rn	rn	NOUN
ejpam-5611	215	5	,	,	PUNCT
ejpam-5611	215	6	then	then	ADV
ejpam-5611	215	7	the	the	DET
ejpam-5611	215	8	pu	pu	PROPN
ejpam-5611	215	9	integral	integral	ADJ
ejpam-5611	215	10	(	(	PUNCT
ejpam-5611	215	11	p	p	NOUN
ejpam-5611	215	12	)	)	PUNCT
ejpam-5611	215	13	∫	∫	PROPN
ejpam-5611	216	1	[	[	X
ejpam-5611	216	2	a	a	X
ejpam-5611	216	3	,	,	PUNCT
ejpam-5611	216	4	b	b	NOUN
ejpam-5611	216	5	]	]	X
ejpam-5611	216	6	f	f	X
ejpam-5611	216	7	·	·	PUNCT
ejpam-5611	216	8	ϕ	ϕ	PROPN
ejpam-5611	216	9	exists	exist	VERB
ejpam-5611	216	10	for	for	ADP
ejpam-5611	216	11	any	any	DET
ejpam-5611	216	12	continuously	continuously	ADV
ejpam-5611	216	13	differentiable	differentiable	ADJ
ejpam-5611	216	14	function	function	NOUN
ejpam-5611	216	15	ϕ	ϕ	NOUN
ejpam-5611	216	16	:	:	PUNCT
ejpam-5611	216	17	g	g	NOUN
ejpam-5611	216	18	→	→	SYM
ejpam-5611	216	19	r	r	NOUN
ejpam-5611	216	20	with	with	ADP
ejpam-5611	216	21	0	0	NUM
ejpam-5611	216	22	<	<	X
ejpam-5611	216	23	ϕ(x	ϕ(x	X
ejpam-5611	216	24	)	)	PUNCT
ejpam-5611	216	25	≤	≤	NUM
ejpam-5611	216	26	1	1	NUM
ejpam-5611	216	27	,	,	PUNCT
ejpam-5611	216	28	for	for	ADP
ejpam-5611	216	29	all	all	DET
ejpam-5611	216	30	x	x	SYM
ejpam-5611	216	31	∈	∈	PROPN
ejpam-5611	216	32	g.	g.	PROPN
ejpam-5611	216	33	g.	g.	PROPN
ejpam-5611	216	34	flores	flores	PROPN
ejpam-5611	216	35	,	,	PUNCT
ejpam-5611	216	36	a.	a.	PROPN
ejpam-5611	216	37	flores	flores	PROPN
ejpam-5611	216	38	/	/	SYM
ejpam-5611	216	39	eur	eur	PROPN
ejpam-5611	216	40	.	.	PUNCT
ejpam-5611	217	1	j.	j.	PROPN
ejpam-5611	217	2	pure	pure	PROPN
ejpam-5611	217	3	appl	appl	PROPN
ejpam-5611	217	4	.	.	PROPN
ejpam-5611	217	5	math	math	PROPN
ejpam-5611	217	6	,	,	PUNCT
ejpam-5611	217	7	18	18	NUM
ejpam-5611	217	8	(	(	PUNCT
ejpam-5611	217	9	2	2	NUM
ejpam-5611	217	10	)	)	PUNCT
ejpam-5611	217	11	(	(	PUNCT
ejpam-5611	217	12	2025	2025	NUM
ejpam-5611	217	13	)	)	PUNCT
ejpam-5611	217	14	,	,	PUNCT
ejpam-5611	217	15	5611	5611	NUM
ejpam-5611	217	16	10	10	NUM
ejpam-5611	217	17	of	of	ADP
ejpam-5611	217	18	16	16	NUM
ejpam-5611	217	19	proof	proof	NOUN
ejpam-5611	217	20	:	:	PUNCT
ejpam-5611	217	21	fix	fix	VERB
ejpam-5611	217	22	ϵ	ϵ	X
ejpam-5611	217	23	>	>	X
ejpam-5611	217	24	0	0	NUM
ejpam-5611	217	25	.	.	PUNCT
ejpam-5611	218	1	then	then	ADV
ejpam-5611	218	2	we	we	PRON
ejpam-5611	218	3	choose	choose	VERB
ejpam-5611	218	4	a	a	DET
ejpam-5611	218	5	gauge	gauge	ADJ
ejpam-5611	218	6	δ1	δ1	NOUN
ejpam-5611	218	7	on	on	ADP
ejpam-5611	218	8	[	[	X
ejpam-5611	218	9	a	a	DET
ejpam-5611	218	10	,	,	PUNCT
ejpam-5611	218	11	b	b	NOUN
ejpam-5611	218	12	]	]	X
ejpam-5611	218	13	such	such	ADJ
ejpam-5611	218	14	that	that	SCONJ
ejpam-5611	218	15	for	for	ADP
ejpam-5611	218	16	any	any	DET
ejpam-5611	218	17	δ1	δ1	NOUN
ejpam-5611	218	18	-	-	PUNCT
ejpam-5611	218	19	fine	fine	NOUN
ejpam-5611	218	20	division	division	NOUN
ejpam-5611	218	21	d	d	NOUN
ejpam-5611	218	22	=	=	PRON
ejpam-5611	218	23	{	{	PUNCT
ejpam-5611	218	24	(	(	PUNCT
ejpam-5611	218	25	ξ	ξ	PROPN
ejpam-5611	218	26	,	,	PUNCT
ejpam-5611	218	27	φ	φ	PROPN
ejpam-5611	218	28	,	,	PUNCT
ejpam-5611	218	29	i	i	NOUN
ejpam-5611	218	30	)	)	PUNCT
ejpam-5611	218	31	}	}	PUNCT
ejpam-5611	218	32	of	of	ADP
ejpam-5611	218	33	[	[	X
ejpam-5611	218	34	a	a	X
ejpam-5611	218	35	,	,	PUNCT
ejpam-5611	218	36	b	b	NOUN
ejpam-5611	218	37	]	]	X
ejpam-5611	218	38	,	,	PUNCT
ejpam-5611	218	39	we	we	PRON
ejpam-5611	218	40	have∥∥∥∥∑	have∥∥∥∥∑	PUNCT
ejpam-5611	218	41	d	d	ADJ
ejpam-5611	218	42	f(ξ	f(ξ	NOUN
ejpam-5611	218	43	)	)	PUNCT
ejpam-5611	218	44	∫	∫	NOUN
ejpam-5611	219	1	i	i	PRON
ejpam-5611	219	2	φ−	φ−	PROPN
ejpam-5611	219	3	(	(	PUNCT
ejpam-5611	219	4	p	p	NOUN
ejpam-5611	219	5	)	)	PUNCT
ejpam-5611	219	6	∫	∫	PROPN
ejpam-5611	220	1	[	[	X
ejpam-5611	220	2	a	a	X
ejpam-5611	220	3	,	,	PUNCT
ejpam-5611	220	4	b	b	NOUN
ejpam-5611	220	5	]	]	X
ejpam-5611	220	6	f	f	X
ejpam-5611	220	7	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5611	220	8	<	<	X
ejpam-5611	220	9	ϵ.	ϵ.	NOUN
ejpam-5611	220	10	assume	assume	VERB
ejpam-5611	220	11	that	that	SCONJ
ejpam-5611	220	12	b(x	b(x	NOUN
ejpam-5611	220	13	,	,	PUNCT
ejpam-5611	220	14	δ1(x	δ1(x	NOUN
ejpam-5611	220	15	)	)	PUNCT
ejpam-5611	220	16	)	)	PUNCT
ejpam-5611	221	1	⊆	⊆	NUM
ejpam-5611	221	2	g	g	NOUN
ejpam-5611	221	3	,	,	PUNCT
ejpam-5611	221	4	for	for	ADP
ejpam-5611	221	5	each	each	DET
ejpam-5611	221	6	x	x	SYM
ejpam-5611	221	7	∈	∈	PROPN
ejpam-5611	221	8	supp	supp	PROPN
ejpam-5611	221	9	f	f	PROPN
ejpam-5611	221	10	.	.	PUNCT
ejpam-5611	222	1	put	put	VERB
ejpam-5611	222	2	m	m	PROPN
ejpam-5611	222	3	=	=	SYM
ejpam-5611	222	4	v	v	ADJ
ejpam-5611	222	5	(	(	PUNCT
ejpam-5611	222	6	g	g	NOUN
ejpam-5611	222	7	;	;	PUNCT
ejpam-5611	222	8	[	[	X
ejpam-5611	222	9	a	a	X
ejpam-5611	222	10	,	,	PUNCT
ejpam-5611	222	11	b	b	NOUN
ejpam-5611	222	12	]	]	X
ejpam-5611	222	13	)	)	PUNCT
ejpam-5611	222	14	∈	∈	PROPN
ejpam-5611	222	15	r	r	NOUN
ejpam-5611	223	1	and	and	CCONJ
ejpam-5611	223	2	we	we	PRON
ejpam-5611	223	3	choose	choose	VERB
ejpam-5611	223	4	δ2(x	δ2(x	PROPN
ejpam-5611	223	5	)	)	PUNCT
ejpam-5611	223	6	>	>	X
ejpam-5611	223	7	0	0	NUM
ejpam-5611	224	1	such	such	ADJ
ejpam-5611	224	2	that	that	PRON
ejpam-5611	224	3	for	for	ADP
ejpam-5611	224	4	any	any	DET
ejpam-5611	224	5	y	y	PROPN
ejpam-5611	224	6	∈	∈	PROPN
ejpam-5611	224	7	[	[	X
ejpam-5611	224	8	a	a	X
ejpam-5611	224	9	,	,	PUNCT
ejpam-5611	224	10	b	b	NOUN
ejpam-5611	224	11	]	]	X
ejpam-5611	224	12	with	with	ADP
ejpam-5611	224	13	y	y	PROPN
ejpam-5611	224	14	∈	∈	PROPN
ejpam-5611	224	15	b(x	b(x	NOUN
ejpam-5611	224	16	,	,	PUNCT
ejpam-5611	224	17	δ2(x	δ2(x	NOUN
ejpam-5611	224	18	)	)	PUNCT
ejpam-5611	224	19	)	)	PUNCT
ejpam-5611	224	20	,	,	PUNCT
ejpam-5611	224	21	we	we	PRON
ejpam-5611	224	22	have	have	VERB
ejpam-5611	224	23	∥f(x)∥	∥f(x)∥	NOUN
ejpam-5611	224	24	·	·	PUNCT
ejpam-5611	224	25	|ϕ(y)−	|ϕ(y)−	VERB
ejpam-5611	225	1	ϕ(x)|	ϕ(x)|	ADP
ejpam-5611	225	2	<	<	X
ejpam-5611	225	3	ϵ	ϵ	X
ejpam-5611	225	4	3(m	3(m	NUM
ejpam-5611	225	5	+	+	CCONJ
ejpam-5611	225	6	1	1	NUM
ejpam-5611	225	7	)	)	PUNCT
ejpam-5611	225	8	.	.	PUNCT
ejpam-5611	226	1	(	(	PUNCT
ejpam-5611	226	2	3.12	3.12	NUM
ejpam-5611	226	3	)	)	PUNCT
ejpam-5611	226	4	take	take	VERB
ejpam-5611	226	5	δ(x	δ(x	NOUN
ejpam-5611	226	6	)	)	PUNCT
ejpam-5611	226	7	=	=	SYM
ejpam-5611	226	8	min{δ1(x	min{δ1(x	PROPN
ejpam-5611	226	9	)	)	PUNCT
ejpam-5611	226	10	,	,	PUNCT
ejpam-5611	226	11	δ2(x	δ2(x	NOUN
ejpam-5611	226	12	)	)	PUNCT
ejpam-5611	226	13	}	}	PUNCT
ejpam-5611	226	14	,	,	PUNCT
ejpam-5611	226	15	for	for	ADP
ejpam-5611	226	16	all	all	DET
ejpam-5611	226	17	x	x	SYM
ejpam-5611	226	18	∈	∈	PROPN
ejpam-5611	226	19	supp	supp	PROPN
ejpam-5611	226	20	f	f	PROPN
ejpam-5611	226	21	.	.	PUNCT
ejpam-5611	227	1	note	note	VERB
ejpam-5611	227	2	that	that	SCONJ
ejpam-5611	227	3	for	for	ADP
ejpam-5611	227	4	each	each	DET
ejpam-5611	227	5	x	x	SYM
ejpam-5611	227	6	∈	∈	PROPN
ejpam-5611	227	7	supp	supp	PROPN
ejpam-5611	227	8	f	f	PROPN
ejpam-5611	227	9	,	,	PUNCT
ejpam-5611	227	10	if	if	SCONJ
ejpam-5611	227	11	y	y	PROPN
ejpam-5611	227	12	∈	∈	PROPN
ejpam-5611	227	13	b(x	b(x	NOUN
ejpam-5611	227	14	,	,	PUNCT
ejpam-5611	227	15	δ(x	δ(x	NOUN
ejpam-5611	227	16	)	)	PUNCT
ejpam-5611	227	17	)	)	PUNCT
ejpam-5611	227	18	,	,	PUNCT
ejpam-5611	227	19	the	the	DET
ejpam-5611	227	20	inequality	inequality	NOUN
ejpam-5611	227	21	(	(	PUNCT
ejpam-5611	227	22	3.12	3.12	NUM
ejpam-5611	227	23	)	)	PUNCT
ejpam-5611	227	24	still	still	ADV
ejpam-5611	227	25	holds	hold	VERB
ejpam-5611	227	26	.	.	PUNCT
ejpam-5611	228	1	for	for	ADP
ejpam-5611	228	2	each	each	DET
ejpam-5611	228	3	x	x	SYM
ejpam-5611	228	4	∈	∈	PROPN
ejpam-5611	228	5	supp	supp	PROPN
ejpam-5611	228	6	f	f	PROPN
ejpam-5611	228	7	,	,	PUNCT
ejpam-5611	228	8	we	we	PRON
ejpam-5611	228	9	have	have	VERB
ejpam-5611	228	10	∥f(x)∥	∥f(x)∥	NOUN
ejpam-5611	228	11	·	·	PUNCT
ejpam-5611	228	12	sup{|ϕ(y)−	sup{|ϕ(y)−	ADJ
ejpam-5611	228	13	ϕ(x)|	ϕ(x)|	ADV
ejpam-5611	228	14	:	:	PUNCT
ejpam-5611	228	15	y	y	PROPN
ejpam-5611	228	16	∈	∈	PROPN
ejpam-5611	228	17	b(x	b(x	NOUN
ejpam-5611	228	18	,	,	PUNCT
ejpam-5611	228	19	δ(x	δ(x	NOUN
ejpam-5611	228	20	)	)	PUNCT
ejpam-5611	228	21	)	)	PUNCT
ejpam-5611	228	22	}	}	PUNCT
ejpam-5611	229	1	<	<	X
ejpam-5611	229	2	ϵ	ϵ	X
ejpam-5611	229	3	3(m	3(m	NUM
ejpam-5611	229	4	+	+	CCONJ
ejpam-5611	229	5	1	1	X
ejpam-5611	229	6	)	)	PUNCT
ejpam-5611	229	7	(	(	PUNCT
ejpam-5611	229	8	3.13	3.13	NUM
ejpam-5611	229	9	)	)	PUNCT
ejpam-5611	229	10	now	now	ADV
ejpam-5611	229	11	,	,	PUNCT
ejpam-5611	229	12	let	let	VERB
ejpam-5611	229	13	d1	d1	PROPN
ejpam-5611	229	14	=	=	SYM
ejpam-5611	229	15	{	{	PUNCT
ejpam-5611	229	16	(	(	PUNCT
ejpam-5611	229	17	ξ	ξ	PROPN
ejpam-5611	229	18	,	,	PUNCT
ejpam-5611	229	19	φ	φ	PROPN
ejpam-5611	229	20	,	,	PUNCT
ejpam-5611	229	21	i	i	NOUN
ejpam-5611	229	22	)	)	PUNCT
ejpam-5611	229	23	}	}	PUNCT
ejpam-5611	229	24	and	and	CCONJ
ejpam-5611	229	25	d2	d2	PROPN
ejpam-5611	229	26	=	=	SYM
ejpam-5611	229	27	{	{	PUNCT
ejpam-5611	229	28	(	(	PUNCT
ejpam-5611	229	29	η	η	PROPN
ejpam-5611	229	30	,	,	PUNCT
ejpam-5611	229	31	ψ	ψ	PROPN
ejpam-5611	229	32	,	,	PUNCT
ejpam-5611	229	33	j	j	NOUN
ejpam-5611	229	34	)	)	PUNCT
ejpam-5611	229	35	}	}	PUNCT
ejpam-5611	229	36	be	be	AUX
ejpam-5611	229	37	any	any	DET
ejpam-5611	229	38	δ	δ	NOUN
ejpam-5611	229	39	-	-	PUNCT
ejpam-5611	229	40	fine	fine	ADJ
ejpam-5611	229	41	divisions	division	NOUN
ejpam-5611	229	42	of	of	ADP
ejpam-5611	229	43	[	[	X
ejpam-5611	229	44	a	a	X
ejpam-5611	229	45	,	,	PUNCT
ejpam-5611	229	46	b	b	NOUN
ejpam-5611	229	47	]	]	X
ejpam-5611	229	48	.	.	PUNCT
ejpam-5611	230	1	for	for	ADP
ejpam-5611	230	2	each	each	DET
ejpam-5611	230	3	x	x	SYM
ejpam-5611	230	4	∈	∈	PROPN
ejpam-5611	230	5	supp	supp	PROPN
ejpam-5611	230	6	f	f	PROPN
ejpam-5611	230	7	,	,	PUNCT
ejpam-5611	230	8	since	since	SCONJ
ejpam-5611	230	9	0	0	NUM
ejpam-5611	230	10	<	<	X
ejpam-5611	230	11	ϕ(x	ϕ(x	X
ejpam-5611	230	12	)	)	PUNCT
ejpam-5611	230	13	≤	≤	NUM
ejpam-5611	230	14	1	1	NUM
ejpam-5611	230	15	,	,	PUNCT
ejpam-5611	230	16	we	we	PRON
ejpam-5611	230	17	have∑	have∑	VERB
ejpam-5611	230	18	d1	d1	PROPN
ejpam-5611	230	19	ϕ(x	ϕ(x	PROPN
ejpam-5611	230	20	)	)	PUNCT
ejpam-5611	230	21	·	·	PUNCT
ejpam-5611	230	22	φ(x	φ(x	X
ejpam-5611	230	23	)	)	PUNCT
ejpam-5611	230	24	=	=	SYM
ejpam-5611	230	25	ϕ(x	ϕ(x	X
ejpam-5611	230	26	)	)	PUNCT
ejpam-5611	230	27	·	·	PUNCT
ejpam-5611	230	28	∑	∑	PUNCT
ejpam-5611	230	29	d1	d1	PROPN
ejpam-5611	230	30	φ(x	φ(x	NOUN
ejpam-5611	230	31	)	)	PUNCT
ejpam-5611	230	32	=	=	SYM
ejpam-5611	230	33	ϕ(x	ϕ(x	X
ejpam-5611	230	34	)	)	PUNCT
ejpam-5611	230	35	≤	≤	NUM
ejpam-5611	230	36	1	1	NUM
ejpam-5611	230	37	.	.	PUNCT
ejpam-5611	231	1	so	so	ADV
ejpam-5611	231	2	,	,	PUNCT
ejpam-5611	231	3	{	{	PUNCT
ejpam-5611	231	4	ϕ	ϕ	X
ejpam-5611	231	5	·	·	PUNCT
ejpam-5611	231	6	φ	φ	NUM
ejpam-5611	231	7	}	}	PUNCT
ejpam-5611	231	8	is	be	AUX
ejpam-5611	231	9	a	a	DET
ejpam-5611	231	10	partial	partial	ADJ
ejpam-5611	231	11	partition	partition	NOUN
ejpam-5611	231	12	of	of	ADP
ejpam-5611	231	13	unity	unity	NOUN
ejpam-5611	231	14	on	on	ADP
ejpam-5611	231	15	supp	supp	PROPN
ejpam-5611	231	16	f	f	PROPN
ejpam-5611	231	17	.	.	PUNCT
ejpam-5611	232	1	since	since	SCONJ
ejpam-5611	232	2	ϕ(x	ϕ(x	PROPN
ejpam-5611	232	3	)	)	PUNCT
ejpam-5611	232	4	>	>	X
ejpam-5611	232	5	0	0	PUNCT
ejpam-5611	232	6	for	for	ADP
ejpam-5611	232	7	all	all	DET
ejpam-5611	232	8	x	x	SYM
ejpam-5611	232	9	∈	∈	PROPN
ejpam-5611	232	10	g	g	NOUN
ejpam-5611	232	11	,	,	PUNCT
ejpam-5611	232	12	it	it	PRON
ejpam-5611	232	13	is	be	AUX
ejpam-5611	232	14	evident	evident	ADJ
ejpam-5611	232	15	that	that	SCONJ
ejpam-5611	232	16	supp	supp	NOUN
ejpam-5611	232	17	(	(	PUNCT
ejpam-5611	232	18	ϕ	ϕ	PROPN
ejpam-5611	232	19	·	·	PUNCT
ejpam-5611	232	20	φ	φ	NUM
ejpam-5611	232	21	)	)	PUNCT
ejpam-5611	232	22	=	=	SYM
ejpam-5611	232	23	supp	supp	NOUN
ejpam-5611	232	24	(	(	PUNCT
ejpam-5611	232	25	φ	φ	NOUN
ejpam-5611	232	26	)	)	PUNCT
ejpam-5611	232	27	.	.	PUNCT
ejpam-5611	233	1	note	note	VERB
ejpam-5611	233	2	that	that	SCONJ
ejpam-5611	233	3	d1	d1	PROPN
ejpam-5611	233	4	is	be	AUX
ejpam-5611	233	5	a	a	DET
ejpam-5611	233	6	δ	δ	NOUN
ejpam-5611	233	7	-	-	PUNCT
ejpam-5611	233	8	fine	fine	ADJ
ejpam-5611	233	9	division	division	NOUN
ejpam-5611	233	10	of	of	ADP
ejpam-5611	233	11	[	[	X
ejpam-5611	233	12	a	a	X
ejpam-5611	233	13	,	,	PUNCT
ejpam-5611	233	14	b	b	NOUN
ejpam-5611	233	15	]	]	PUNCT
ejpam-5611	233	16	.	.	PUNCT
ejpam-5611	234	1	then	then	ADV
ejpam-5611	234	2	supp	supp	PROPN
ejpam-5611	234	3	(	(	PUNCT
ejpam-5611	234	4	ϕ	ϕ	PROPN
ejpam-5611	234	5	·	·	PUNCT
ejpam-5611	234	6	φ	φ	NUM
ejpam-5611	234	7	)	)	PUNCT
ejpam-5611	234	8	=	=	SYM
ejpam-5611	234	9	supp	supp	PROPN
ejpam-5611	234	10	φ	φ	PROPN
ejpam-5611	234	11	⊆	⊆	NUM
ejpam-5611	234	12	i	i	PROPN
ejpam-5611	234	13	⊆	⊆	NUM
ejpam-5611	234	14	b(ξ	b(ξ	NOUN
ejpam-5611	234	15	,	,	PUNCT
ejpam-5611	234	16	δ(ξ	δ(ξ	NOUN
ejpam-5611	234	17	)	)	PUNCT
ejpam-5611	234	18	)	)	PUNCT
ejpam-5611	234	19	.	.	PUNCT
ejpam-5611	235	1	hence	hence	ADV
ejpam-5611	235	2	,	,	PUNCT
ejpam-5611	235	3	{	{	PUNCT
ejpam-5611	235	4	(	(	PUNCT
ejpam-5611	235	5	ξ	ξ	PROPN
ejpam-5611	235	6	,	,	PUNCT
ejpam-5611	235	7	ϕ	ϕ	X
ejpam-5611	235	8	·	·	PUNCT
ejpam-5611	235	9	φ	φ	NUM
ejpam-5611	235	10	,	,	PUNCT
ejpam-5611	235	11	i	i	NOUN
ejpam-5611	235	12	)	)	PUNCT
ejpam-5611	235	13	}	}	PUNCT
ejpam-5611	235	14	is	be	AUX
ejpam-5611	235	15	a	a	DET
ejpam-5611	235	16	partial	partial	ADJ
ejpam-5611	235	17	δ	δ	NOUN
ejpam-5611	235	18	-	-	PUNCT
ejpam-5611	235	19	fine	fine	ADJ
ejpam-5611	235	20	division	division	NOUN
ejpam-5611	235	21	of	of	ADP
ejpam-5611	235	22	[	[	X
ejpam-5611	235	23	a	a	X
ejpam-5611	235	24	,	,	PUNCT
ejpam-5611	235	25	b	b	NOUN
ejpam-5611	235	26	]	]	X
ejpam-5611	235	27	.	.	PUNCT
ejpam-5611	236	1	since	since	SCONJ
ejpam-5611	236	2	0	0	NUM
ejpam-5611	236	3	<	<	X
ejpam-5611	236	4	ϕ(x	ϕ(x	X
ejpam-5611	236	5	)	)	PUNCT
ejpam-5611	236	6	≤	≤	NOUN
ejpam-5611	236	7	1	1	NUM
ejpam-5611	236	8	for	for	ADP
ejpam-5611	236	9	all	all	DET
ejpam-5611	236	10	supp	supp	PROPN
ejpam-5611	236	11	f	f	PROPN
ejpam-5611	236	12	,	,	PUNCT
ejpam-5611	236	13	∑	∑	PROPN
ejpam-5611	236	14	d2	d2	PROPN
ejpam-5611	236	15	(	(	PUNCT
ejpam-5611	236	16	1−	1−	NUM
ejpam-5611	236	17	ϕ(x	ϕ(x	NOUN
ejpam-5611	236	18	)	)	PUNCT
ejpam-5611	236	19	)	)	PUNCT
ejpam-5611	236	20	·	·	PUNCT
ejpam-5611	236	21	ψ(x	ψ(x	NOUN
ejpam-5611	236	22	)	)	PUNCT
ejpam-5611	236	23	=	=	PUNCT
ejpam-5611	236	24	(	(	PUNCT
ejpam-5611	236	25	1−	1−	NUM
ejpam-5611	236	26	ϕ(x	ϕ(x	NOUN
ejpam-5611	236	27	)	)	PUNCT
ejpam-5611	236	28	)	)	PUNCT
ejpam-5611	236	29	·	·	PUNCT
ejpam-5611	236	30	∑	∑	PUNCT
ejpam-5611	236	31	d2	d2	PROPN
ejpam-5611	236	32	ψ(x	ψ(x	NOUN
ejpam-5611	236	33	)	)	PUNCT
ejpam-5611	236	34	=	=	SYM
ejpam-5611	236	35	1−	1−	NUM
ejpam-5611	236	36	ϕ(x	ϕ(x	NOUN
ejpam-5611	236	37	)	)	PUNCT
ejpam-5611	236	38	≤	≤	NUM
ejpam-5611	237	1	1	1	NUM
ejpam-5611	238	1	.	.	PUNCT
ejpam-5611	239	1	so	so	ADV
ejpam-5611	239	2	,	,	PUNCT
ejpam-5611	239	3	{	{	PUNCT
ejpam-5611	239	4	(	(	PUNCT
ejpam-5611	239	5	1−	1−	NUM
ejpam-5611	239	6	ϕ	ϕ	NOUN
ejpam-5611	239	7	)	)	PUNCT
ejpam-5611	239	8	·	·	PUNCT
ejpam-5611	240	1	ψ	ψ	X
ejpam-5611	240	2	)	)	PUNCT
ejpam-5611	240	3	}	}	PUNCT
ejpam-5611	240	4	is	be	AUX
ejpam-5611	240	5	a	a	DET
ejpam-5611	240	6	partial	partial	ADJ
ejpam-5611	240	7	partition	partition	NOUN
ejpam-5611	240	8	of	of	ADP
ejpam-5611	240	9	unity	unity	NOUN
ejpam-5611	240	10	on	on	ADP
ejpam-5611	240	11	supp	supp	PROPN
ejpam-5611	240	12	f	f	PROPN
ejpam-5611	240	13	.	.	PUNCT
ejpam-5611	241	1	moreover	moreover	ADV
ejpam-5611	241	2	,	,	PUNCT
ejpam-5611	241	3	supp	supp	PROPN
ejpam-5611	241	4	(	(	PUNCT
ejpam-5611	241	5	1−	1−	NUM
ejpam-5611	241	6	ϕ	ϕ	NOUN
ejpam-5611	241	7	)	)	PUNCT
ejpam-5611	241	8	·	·	PUNCT
ejpam-5611	241	9	ψ	ψ	X
ejpam-5611	241	10	=	=	SYM
ejpam-5611	241	11	supp	supp	PROPN
ejpam-5611	241	12	ψ	ψ	ADP
ejpam-5611	241	13	⊆	⊆	NUM
ejpam-5611	241	14	j	j	PROPN
ejpam-5611	241	15	⊆	⊆	NUM
ejpam-5611	241	16	b(η	b(η	NOUN
ejpam-5611	241	17	,	,	PUNCT
ejpam-5611	241	18	δ(η	δ(η	PROPN
ejpam-5611	241	19	)	)	PUNCT
ejpam-5611	241	20	)	)	PUNCT
ejpam-5611	241	21	.	.	PUNCT
ejpam-5611	242	1	hence	hence	ADV
ejpam-5611	242	2	,	,	PUNCT
ejpam-5611	242	3	{	{	PUNCT
ejpam-5611	242	4	(	(	PUNCT
ejpam-5611	242	5	η	η	PROPN
ejpam-5611	242	6	,	,	PUNCT
ejpam-5611	242	7	(	(	PUNCT
ejpam-5611	242	8	1	1	NUM
ejpam-5611	242	9	−	−	PROPN
ejpam-5611	242	10	ϕ	ϕ	NOUN
ejpam-5611	242	11	)	)	PUNCT
ejpam-5611	242	12	·	·	PUNCT
ejpam-5611	243	1	ψ	ψ	X
ejpam-5611	243	2	,	,	PUNCT
ejpam-5611	243	3	j	j	NOUN
ejpam-5611	243	4	)	)	PUNCT
ejpam-5611	243	5	}	}	PUNCT
ejpam-5611	243	6	is	be	AUX
ejpam-5611	243	7	a	a	DET
ejpam-5611	243	8	partial	partial	ADJ
ejpam-5611	243	9	δ	δ	NOUN
ejpam-5611	243	10	-	-	PUNCT
ejpam-5611	243	11	fine	fine	ADJ
ejpam-5611	243	12	division	division	NOUN
ejpam-5611	243	13	of	of	ADP
ejpam-5611	243	14	[	[	X
ejpam-5611	243	15	a	a	X
ejpam-5611	243	16	,	,	PUNCT
ejpam-5611	243	17	b	b	NOUN
ejpam-5611	243	18	]	]	X
ejpam-5611	243	19	which	which	PRON
ejpam-5611	243	20	,	,	PUNCT
ejpam-5611	243	21	by	by	ADP
ejpam-5611	243	22	lemma	lemma	PROPN
ejpam-5611	243	23	2	2	NUM
ejpam-5611	243	24	,	,	PUNCT
ejpam-5611	243	25	will	will	AUX
ejpam-5611	243	26	further	far	ADV
ejpam-5611	243	27	imply	imply	VERB
ejpam-5611	243	28	that	that	SCONJ
ejpam-5611	243	29	{	{	PUNCT
ejpam-5611	243	30	(	(	PUNCT
ejpam-5611	243	31	ξ	ξ	PROPN
ejpam-5611	243	32	,	,	PUNCT
ejpam-5611	243	33	ϕ	ϕ	X
ejpam-5611	243	34	·	·	PUNCT
ejpam-5611	243	35	φ	φ	NUM
ejpam-5611	243	36	,	,	PUNCT
ejpam-5611	243	37	i	i	NOUN
ejpam-5611	243	38	)	)	PUNCT
ejpam-5611	243	39	}	}	PUNCT
ejpam-5611	243	40	∪	∪	X
ejpam-5611	243	41	{	{	PUNCT
ejpam-5611	243	42	(	(	PUNCT
ejpam-5611	243	43	η	η	PROPN
ejpam-5611	243	44	,	,	PUNCT
ejpam-5611	243	45	(	(	PUNCT
ejpam-5611	243	46	1−	1−	NUM
ejpam-5611	243	47	ϕ	ϕ	NOUN
ejpam-5611	243	48	)	)	PUNCT
ejpam-5611	243	49	·	·	PUNCT
ejpam-5611	244	1	ψ	ψ	X
ejpam-5611	244	2	,	,	PUNCT
ejpam-5611	244	3	j	j	NOUN
ejpam-5611	244	4	)	)	PUNCT
ejpam-5611	244	5	}	}	PUNCT
ejpam-5611	244	6	is	be	AUX
ejpam-5611	244	7	δ	δ	PROPN
ejpam-5611	244	8	-	-	PUNCT
ejpam-5611	244	9	fine	fine	ADJ
ejpam-5611	244	10	division	division	NOUN
ejpam-5611	244	11	of	of	ADP
ejpam-5611	244	12	[	[	X
ejpam-5611	244	13	a	a	X
ejpam-5611	244	14	,	,	PUNCT
ejpam-5611	244	15	b	b	NOUN
ejpam-5611	244	16	]	]	X
ejpam-5611	244	17	.	.	PUNCT
ejpam-5611	245	1	but	but	CCONJ
ejpam-5611	245	2	f	f	PROPN
ejpam-5611	245	3	is	be	AUX
ejpam-5611	245	4	pu	pu	PROPN
ejpam-5611	245	5	integrability	integrability	NOUN
ejpam-5611	245	6	over	over	ADP
ejpam-5611	245	7	[	[	X
ejpam-5611	245	8	a	a	DET
ejpam-5611	245	9	,	,	PUNCT
ejpam-5611	245	10	b	b	NOUN
ejpam-5611	245	11	]	]	X
ejpam-5611	245	12	;	;	PUNCT
ejpam-5611	245	13	so,∥∥∥∥(∑	so,∥∥∥∥(∑	NOUN
ejpam-5611	245	14	d1	d1	PROPN
ejpam-5611	245	15	f(ξ	f(ξ	PROPN
ejpam-5611	245	16	)	)	PUNCT
ejpam-5611	245	17	∫	∫	PROPN
ejpam-5611	246	1	i	i	PRON
ejpam-5611	246	2	ϕ	ϕ	PROPN
ejpam-5611	246	3	·	·	PUNCT
ejpam-5611	246	4	φ	φ	PROPN
ejpam-5611	246	5	+	+	CCONJ
ejpam-5611	246	6	∑	∑	PROPN
ejpam-5611	246	7	d2	d2	PROPN
ejpam-5611	246	8	f(η	f(η	PROPN
ejpam-5611	246	9	)	)	PUNCT
ejpam-5611	247	1	∫	∫	PROPN
ejpam-5611	247	2	j	j	PROPN
ejpam-5611	247	3	(	(	PUNCT
ejpam-5611	247	4	1−	1−	NUM
ejpam-5611	247	5	ϕ	ϕ	NOUN
ejpam-5611	247	6	)	)	PUNCT
ejpam-5611	247	7	·	·	PUNCT
ejpam-5611	247	8	ψ	ψ	X
ejpam-5611	247	9	)	)	PUNCT
ejpam-5611	247	10	−	−	PROPN
ejpam-5611	248	1	(	(	PUNCT
ejpam-5611	248	2	p	p	NOUN
ejpam-5611	248	3	)	)	PUNCT
ejpam-5611	248	4	∫	∫	PROPN
ejpam-5611	249	1	[	[	X
ejpam-5611	249	2	a	a	X
ejpam-5611	249	3	,	,	PUNCT
ejpam-5611	249	4	b	b	NOUN
ejpam-5611	249	5	]	]	X
ejpam-5611	249	6	f	f	X
ejpam-5611	249	7	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5611	249	8	<	<	X
ejpam-5611	249	9	ϵ	ϵ	X
ejpam-5611	249	10	6	6	NUM
ejpam-5611	249	11	.	.	PUNCT
ejpam-5611	250	1	(	(	PUNCT
ejpam-5611	250	2	3.14	3.14	NUM
ejpam-5611	250	3	)	)	PUNCT
ejpam-5611	250	4	g.	g.	PROPN
ejpam-5611	250	5	flores	flores	PROPN
ejpam-5611	250	6	,	,	PUNCT
ejpam-5611	250	7	a.	a.	PROPN
ejpam-5611	250	8	flores	flores	PROPN
ejpam-5611	250	9	/	/	SYM
ejpam-5611	250	10	eur	eur	PROPN
ejpam-5611	250	11	.	.	PUNCT
ejpam-5611	251	1	j.	j.	PROPN
ejpam-5611	251	2	pure	pure	PROPN
ejpam-5611	251	3	appl	appl	PROPN
ejpam-5611	251	4	.	.	PROPN
ejpam-5611	251	5	math	math	PROPN
ejpam-5611	251	6	,	,	PUNCT
ejpam-5611	251	7	18	18	NUM
ejpam-5611	251	8	(	(	PUNCT
ejpam-5611	251	9	2	2	NUM
ejpam-5611	251	10	)	)	PUNCT
ejpam-5611	251	11	(	(	PUNCT
ejpam-5611	251	12	2025	2025	NUM
ejpam-5611	251	13	)	)	PUNCT
ejpam-5611	251	14	,	,	PUNCT
ejpam-5611	251	15	5611	5611	NUM
ejpam-5611	251	16	11	11	NUM
ejpam-5611	251	17	of	of	ADP
ejpam-5611	251	18	16	16	NUM
ejpam-5611	251	19	since	since	SCONJ
ejpam-5611	251	20	f	f	PROPN
ejpam-5611	251	21	is	be	AUX
ejpam-5611	251	22	pu	pu	PROPN
ejpam-5611	251	23	integrable	integrable	ADJ
ejpam-5611	251	24	over	over	ADP
ejpam-5611	251	25	[	[	X
ejpam-5611	251	26	a	a	DET
ejpam-5611	251	27	,	,	PUNCT
ejpam-5611	251	28	b	b	NOUN
ejpam-5611	251	29	]	]	PUNCT
ejpam-5611	251	30	and	and	CCONJ
ejpam-5611	251	31	d2	d2	PROPN
ejpam-5611	251	32	is	be	AUX
ejpam-5611	251	33	a	a	DET
ejpam-5611	251	34	δ	δ	NOUN
ejpam-5611	251	35	-	-	PUNCT
ejpam-5611	251	36	fine	fine	ADJ
ejpam-5611	251	37	division	division	NOUN
ejpam-5611	251	38	of	of	ADP
ejpam-5611	251	39	[	[	X
ejpam-5611	251	40	a	a	X
ejpam-5611	251	41	,	,	PUNCT
ejpam-5611	251	42	b	b	NOUN
ejpam-5611	251	43	]	]	X
ejpam-5611	251	44	,	,	PUNCT
ejpam-5611	251	45	we	we	PRON
ejpam-5611	251	46	then	then	ADV
ejpam-5611	251	47	have∥∥∥∥∑	have∥∥∥∥∑	PROPN
ejpam-5611	251	48	d2	d2	PROPN
ejpam-5611	251	49	f(η	f(η	PROPN
ejpam-5611	251	50	)	)	PUNCT
ejpam-5611	252	1	∫	∫	PROPN
ejpam-5611	253	1	j	j	PROPN
ejpam-5611	253	2	ψ	ψ	X
ejpam-5611	253	3	−	−	PROPN
ejpam-5611	253	4	(	(	PUNCT
ejpam-5611	253	5	p	p	NOUN
ejpam-5611	253	6	)	)	PUNCT
ejpam-5611	253	7	∫	∫	PROPN
ejpam-5611	254	1	[	[	X
ejpam-5611	254	2	a	a	X
ejpam-5611	254	3	,	,	PUNCT
ejpam-5611	254	4	b	b	NOUN
ejpam-5611	254	5	]	]	X
ejpam-5611	254	6	f	f	X
ejpam-5611	254	7	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5611	254	8	<	<	X
ejpam-5611	254	9	ϵ	ϵ	X
ejpam-5611	254	10	6	6	NUM
ejpam-5611	254	11	.	.	PUNCT
ejpam-5611	255	1	(	(	PUNCT
ejpam-5611	255	2	3.15	3.15	NUM
ejpam-5611	255	3	)	)	PUNCT
ejpam-5611	255	4	by	by	ADP
ejpam-5611	255	5	(	(	PUNCT
ejpam-5611	255	6	3.14	3.14	NUM
ejpam-5611	255	7	)	)	PUNCT
ejpam-5611	255	8	and	and	CCONJ
ejpam-5611	255	9	(	(	PUNCT
ejpam-5611	255	10	3.15	3.15	NUM
ejpam-5611	255	11	)	)	PUNCT
ejpam-5611	255	12	,	,	PUNCT
ejpam-5611	255	13	we	we	PRON
ejpam-5611	255	14	have∥∥∥∥∑	have∥∥∥∥∑	VERB
ejpam-5611	255	15	d1	d1	PROPN
ejpam-5611	255	16	f(ξ	f(ξ	NOUN
ejpam-5611	255	17	)	)	PUNCT
ejpam-5611	255	18	∫	∫	PROPN
ejpam-5611	256	1	i	i	PRON
ejpam-5611	256	2	ϕ	ϕ	PROPN
ejpam-5611	256	3	·	·	PUNCT
ejpam-5611	256	4	φ	φ	NUM
ejpam-5611	256	5	−	−	PROPN
ejpam-5611	256	6	∑	∑	PROPN
ejpam-5611	256	7	d2	d2	PROPN
ejpam-5611	256	8	f(η	f(η	PROPN
ejpam-5611	256	9	)	)	PUNCT
ejpam-5611	257	1	∫	∫	PROPN
ejpam-5611	258	1	j	j	PROPN
ejpam-5611	258	2	ϕ	ϕ	PROPN
ejpam-5611	258	3	·	·	PUNCT
ejpam-5611	258	4	ψ	ψ	X
ejpam-5611	258	5	∥∥∥∥	∥∥∥∥	NUM
ejpam-5611	258	6	=	=	SYM
ejpam-5611	258	7	∥∥∥∥(∑	∥∥∥∥(∑	NOUN
ejpam-5611	258	8	d1	d1	PROPN
ejpam-5611	258	9	f(ξ	f(ξ	PROPN
ejpam-5611	258	10	)	)	PUNCT
ejpam-5611	258	11	∫	∫	PROPN
ejpam-5611	259	1	i	i	PRON
ejpam-5611	259	2	ϕ	ϕ	PROPN
ejpam-5611	259	3	·	·	PUNCT
ejpam-5611	259	4	φ	φ	PROPN
ejpam-5611	259	5	+	+	CCONJ
ejpam-5611	259	6	∑	∑	PROPN
ejpam-5611	259	7	d2	d2	PROPN
ejpam-5611	259	8	f(η	f(η	PROPN
ejpam-5611	259	9	)	)	PUNCT
ejpam-5611	260	1	∫	∫	PROPN
ejpam-5611	260	2	j	j	PROPN
ejpam-5611	260	3	(	(	PUNCT
ejpam-5611	260	4	1−	1−	NUM
ejpam-5611	260	5	ϕ	ϕ	NOUN
ejpam-5611	260	6	)	)	PUNCT
ejpam-5611	260	7	·	·	PUNCT
ejpam-5611	260	8	ψ	ψ	X
ejpam-5611	260	9	)	)	PUNCT
ejpam-5611	260	10	−	−	PROPN
ejpam-5611	261	1	(	(	PUNCT
ejpam-5611	261	2	p	p	NOUN
ejpam-5611	261	3	)	)	PUNCT
ejpam-5611	261	4	∫	∫	PROPN
ejpam-5611	262	1	[	[	X
ejpam-5611	262	2	a	a	X
ejpam-5611	262	3	,	,	PUNCT
ejpam-5611	262	4	b	b	NOUN
ejpam-5611	262	5	]	]	X
ejpam-5611	262	6	f	f	X
ejpam-5611	263	1	+	+	CCONJ
ejpam-5611	263	2	(	(	PUNCT
ejpam-5611	263	3	p	p	X
ejpam-5611	263	4	)	)	PUNCT
ejpam-5611	263	5	∫	∫	PROPN
ejpam-5611	264	1	[	[	X
ejpam-5611	264	2	a	a	X
ejpam-5611	264	3	,	,	PUNCT
ejpam-5611	264	4	b	b	X
ejpam-5611	264	5	]	]	X
ejpam-5611	264	6	f	f	X
ejpam-5611	264	7	−	−	PROPN
ejpam-5611	264	8	∑	∑	PROPN
ejpam-5611	264	9	d2	d2	PROPN
ejpam-5611	264	10	f(η	f(η	PROPN
ejpam-5611	264	11	)	)	PUNCT
ejpam-5611	265	1	∫	∫	PROPN
ejpam-5611	266	1	j	j	PROPN
ejpam-5611	266	2	ψ	ψ	PROPN
ejpam-5611	266	3	∥∥∥∥	∥∥∥∥	ADJ
ejpam-5611	266	4	≤	≤	NUM
ejpam-5611	266	5	∥∥∥∥(∑	∥∥∥∥(∑	NOUN
ejpam-5611	266	6	d1	d1	PROPN
ejpam-5611	266	7	f(ξ	f(ξ	PROPN
ejpam-5611	266	8	)	)	PUNCT
ejpam-5611	266	9	∫	∫	PROPN
ejpam-5611	267	1	i	i	PRON
ejpam-5611	267	2	ϕ	ϕ	X
ejpam-5611	267	3	·	·	PUNCT
ejpam-5611	267	4	φ+	φ+	NOUN
ejpam-5611	267	5	∑	∑	PUNCT
ejpam-5611	267	6	d2	d2	PROPN
ejpam-5611	267	7	f(η	f(η	PROPN
ejpam-5611	267	8	)	)	PUNCT
ejpam-5611	268	1	∫	∫	PROPN
ejpam-5611	268	2	j	j	PROPN
ejpam-5611	268	3	(	(	PUNCT
ejpam-5611	268	4	1−	1−	NUM
ejpam-5611	268	5	ϕ	ϕ	NOUN
ejpam-5611	268	6	)	)	PUNCT
ejpam-5611	268	7	·	·	PUNCT
ejpam-5611	268	8	ψ	ψ	X
ejpam-5611	268	9	)	)	PUNCT
ejpam-5611	268	10	−	−	PROPN
ejpam-5611	269	1	(	(	PUNCT
ejpam-5611	269	2	p	p	NOUN
ejpam-5611	269	3	)	)	PUNCT
ejpam-5611	269	4	∫	∫	PROPN
ejpam-5611	270	1	[	[	X
ejpam-5611	270	2	a	a	X
ejpam-5611	270	3	,	,	PUNCT
ejpam-5611	270	4	b	b	NOUN
ejpam-5611	270	5	]	]	X
ejpam-5611	270	6	f	f	X
ejpam-5611	270	7	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5611	271	1	+	+	CCONJ
ejpam-5611	271	2	∥∥∥∥(p	∥∥∥∥(p	NOUN
ejpam-5611	271	3	)	)	PUNCT
ejpam-5611	271	4	∫	∫	PROPN
ejpam-5611	272	1	[	[	X
ejpam-5611	272	2	a	a	X
ejpam-5611	272	3	,	,	PUNCT
ejpam-5611	272	4	b	b	X
ejpam-5611	272	5	]	]	X
ejpam-5611	272	6	f	f	X
ejpam-5611	272	7	−	−	PROPN
ejpam-5611	272	8	∑	∑	INTJ
ejpam-5611	272	9	d2	d2	PROPN
ejpam-5611	272	10	f(ξ	f(ξ	NOUN
ejpam-5611	272	11	)	)	PUNCT
ejpam-5611	272	12	∫	∫	NOUN
ejpam-5611	273	1	i	i	PRON
ejpam-5611	273	2	ψ	ψ	VERB
ejpam-5611	273	3	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-5611	273	4	<	<	X
ejpam-5611	273	5	ϵ	ϵ	X
ejpam-5611	273	6	6	6	NUM
ejpam-5611	274	1	+	+	CCONJ
ejpam-5611	274	2	ϵ	ϵ	SYM
ejpam-5611	274	3	6	6	NUM
ejpam-5611	274	4	=	=	SYM
ejpam-5611	274	5	ϵ	ϵ	SYM
ejpam-5611	274	6	3	3	NUM
ejpam-5611	274	7	,	,	PUNCT
ejpam-5611	274	8	that	that	ADV
ejpam-5611	274	9	is	is	ADV
ejpam-5611	274	10	,	,	PUNCT
ejpam-5611	274	11	∥∥∥∥∑	∥∥∥∥∑	PROPN
ejpam-5611	274	12	d1	d1	PROPN
ejpam-5611	274	13	f(ξ	f(ξ	NOUN
ejpam-5611	274	14	)	)	PUNCT
ejpam-5611	274	15	∫	∫	PROPN
ejpam-5611	275	1	i	i	PRON
ejpam-5611	275	2	ϕ	ϕ	PROPN
ejpam-5611	275	3	·	·	PUNCT
ejpam-5611	275	4	φ−	φ−	PROPN
ejpam-5611	275	5	∑	∑	PUNCT
ejpam-5611	275	6	d2	d2	PROPN
ejpam-5611	275	7	f(η	f(η	PROPN
ejpam-5611	275	8	)	)	PUNCT
ejpam-5611	276	1	∫	∫	PROPN
ejpam-5611	277	1	j	j	PROPN
ejpam-5611	277	2	ϕ	ϕ	PROPN
ejpam-5611	277	3	·	·	PUNCT
ejpam-5611	277	4	ψ	ψ	ADP
ejpam-5611	277	5	∥∥∥∥	∥∥∥∥	NOUN
ejpam-5611	277	6	<	<	X
ejpam-5611	277	7	ϵ	ϵ	X
ejpam-5611	277	8	3	3	NUM
ejpam-5611	277	9	(	(	PUNCT
ejpam-5611	277	10	3.16	3.16	NUM
ejpam-5611	277	11	)	)	PUNCT
ejpam-5611	277	12	further	far	ADV
ejpam-5611	277	13	,	,	PUNCT
ejpam-5611	277	14	by	by	ADP
ejpam-5611	277	15	(	(	PUNCT
ejpam-5611	277	16	3.13)∥∥∥∥∑	3.13)∥∥∥∥∑	NUM
ejpam-5611	277	17	d1	d1	PROPN
ejpam-5611	277	18	f(ξ)ϕ(ξ	f(ξ)ϕ(ξ	NOUN
ejpam-5611	277	19	)	)	PUNCT
ejpam-5611	277	20	∫	∫	PROPN
ejpam-5611	278	1	i	i	PRON
ejpam-5611	278	2	φ−	φ−	PROPN
ejpam-5611	278	3	∑	∑	ADV
ejpam-5611	278	4	d1	d1	PROPN
ejpam-5611	278	5	f(ξ	f(ξ	NOUN
ejpam-5611	278	6	)	)	PUNCT
ejpam-5611	278	7	∫	∫	PROPN
ejpam-5611	279	1	i	i	PRON
ejpam-5611	279	2	ϕ	ϕ	PROPN
ejpam-5611	279	3	·	·	PUNCT
ejpam-5611	279	4	φ	φ	NUM
ejpam-5611	279	5	∥∥∥∥	∥∥∥∥	NUM
ejpam-5611	279	6	=	=	SYM
ejpam-5611	279	7	∥∥∥∥∑	∥∥∥∥∑	PROPN
ejpam-5611	279	8	d1	d1	PROPN
ejpam-5611	279	9	f(ξ	f(ξ	NOUN
ejpam-5611	279	10	)	)	PUNCT
ejpam-5611	279	11	∫	∫	NOUN
ejpam-5611	280	1	i	i	PRON
ejpam-5611	280	2	ϕ(ξ	ϕ(ξ	PROPN
ejpam-5611	280	3	)	)	PUNCT
ejpam-5611	280	4	·	·	PUNCT
ejpam-5611	281	1	φ−	φ−	PROPN
ejpam-5611	281	2	∑	∑	PUNCT
ejpam-5611	281	3	d1	d1	PROPN
ejpam-5611	281	4	f(ξ	f(ξ	NOUN
ejpam-5611	281	5	)	)	PUNCT
ejpam-5611	281	6	∫	∫	PROPN
ejpam-5611	282	1	i	i	PRON
ejpam-5611	282	2	ϕ	ϕ	PROPN
ejpam-5611	282	3	·	·	PUNCT
ejpam-5611	282	4	φ	φ	NUM
ejpam-5611	282	5	∥∥∥∥	∥∥∥∥	NUM
ejpam-5611	282	6	=	=	SYM
ejpam-5611	282	7	∥∥∥∥∑	∥∥∥∥∑	PROPN
ejpam-5611	282	8	d1	d1	PROPN
ejpam-5611	282	9	f(ξ	f(ξ	PROPN
ejpam-5611	282	10	)	)	PUNCT
ejpam-5611	283	1	[	[	PUNCT
ejpam-5611	283	2	∫	∫	PUNCT
ejpam-5611	283	3	i	i	PRON
ejpam-5611	283	4	ϕ(ξ	ϕ(ξ	PROPN
ejpam-5611	283	5	)	)	PUNCT
ejpam-5611	283	6	·	·	PUNCT
ejpam-5611	284	1	φ−	φ−	PROPN
ejpam-5611	284	2	∫	∫	PROPN
ejpam-5611	284	3	i	i	NOUN
ejpam-5611	284	4	ϕ	ϕ	PROPN
ejpam-5611	284	5	·	·	PUNCT
ejpam-5611	284	6	φ	φ	X
ejpam-5611	284	7	]	]	PUNCT
ejpam-5611	284	8	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-5611	284	9	=	=	SYM
ejpam-5611	284	10	∥∥∥∥∑	∥∥∥∥∑	PROPN
ejpam-5611	284	11	d1	d1	PROPN
ejpam-5611	284	12	f(ξ	f(ξ	PROPN
ejpam-5611	284	13	)	)	PUNCT
ejpam-5611	284	14	[	[	PUNCT
ejpam-5611	284	15	∫	∫	INTJ
ejpam-5611	284	16	i	i	PRON
ejpam-5611	284	17	(	(	PUNCT
ejpam-5611	284	18	ϕ(ξ	ϕ(ξ	PROPN
ejpam-5611	284	19	)	)	PUNCT
ejpam-5611	284	20	·	·	PUNCT
ejpam-5611	285	1	φ−	φ−	PROPN
ejpam-5611	285	2	ϕ	ϕ	PROPN
ejpam-5611	285	3	·	·	PUNCT
ejpam-5611	285	4	φ	φ	PROPN
ejpam-5611	285	5	)	)	PUNCT
ejpam-5611	285	6	]	]	PUNCT
ejpam-5611	285	7	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-5611	285	8	=	=	SYM
ejpam-5611	285	9	∥∥∥∥∑	∥∥∥∥∑	PROPN
ejpam-5611	285	10	d1	d1	PROPN
ejpam-5611	285	11	f(ξ	f(ξ	PROPN
ejpam-5611	285	12	)	)	PUNCT
ejpam-5611	285	13	[	[	PUNCT
ejpam-5611	285	14	∫	∫	X
ejpam-5611	285	15	i	i	PRON
ejpam-5611	285	16	(	(	PUNCT
ejpam-5611	285	17	ϕ(ξ)−	ϕ(ξ)−	PROPN
ejpam-5611	285	18	ϕ	ϕ	PROPN
ejpam-5611	285	19	)	)	PUNCT
ejpam-5611	285	20	·	·	PUNCT
ejpam-5611	285	21	φ	φ	X
ejpam-5611	285	22	]	]	PUNCT
ejpam-5611	285	23	∥∥∥∥	∥∥∥∥	NOUN
ejpam-5611	285	24	≤	≤	NUM
ejpam-5611	285	25	∥∥∥∥∑	∥∥∥∥∑	PROPN
ejpam-5611	285	26	d1	d1	PROPN
ejpam-5611	285	27	f(ξ	f(ξ	PROPN
ejpam-5611	285	28	)	)	PUNCT
ejpam-5611	285	29	·	·	PUNCT
ejpam-5611	286	1	∫	∫	INTJ
ejpam-5611	287	1	i	i	PRON
ejpam-5611	287	2	sup	sup	NOUN
ejpam-5611	287	3	{	{	PUNCT
ejpam-5611	287	4	|ϕ(ξ)−	|ϕ(ξ)−	NOUN
ejpam-5611	287	5	ϕ(x)|	ϕ(x)|	VERB
ejpam-5611	287	6	:	:	PUNCT
ejpam-5611	287	7	x	x	SYM
ejpam-5611	287	8	∈	∈	PROPN
ejpam-5611	287	9	b(ξ	b(ξ	NOUN
ejpam-5611	287	10	,	,	PUNCT
ejpam-5611	287	11	δ(ξ	δ(ξ	NOUN
ejpam-5611	287	12	)	)	PUNCT
ejpam-5611	287	13	)	)	PUNCT
ejpam-5611	287	14	}	}	PUNCT
ejpam-5611	287	15	·	·	PUNCT
ejpam-5611	288	1	φ	φ	X
ejpam-5611	288	2	∥∥∥∥	∥∥∥∥	NUM
ejpam-5611	288	3	≤	≤	NUM
ejpam-5611	288	4	∥∥∥∥∑	∥∥∥∥∑	PROPN
ejpam-5611	288	5	d1	d1	PROPN
ejpam-5611	288	6	f(ξ	f(ξ	PROPN
ejpam-5611	288	7	)	)	PUNCT
ejpam-5611	288	8	·	·	PUNCT
ejpam-5611	288	9	sup	sup	X
ejpam-5611	288	10	{	{	PUNCT
ejpam-5611	288	11	|ϕ(ξ)−	|ϕ(ξ)−	NOUN
ejpam-5611	288	12	ϕ(x)|	ϕ(x)|	VERB
ejpam-5611	288	13	:	:	PUNCT
ejpam-5611	288	14	x	x	SYM
ejpam-5611	288	15	∈	∈	PROPN
ejpam-5611	288	16	b(ξ	b(ξ	NOUN
ejpam-5611	288	17	,	,	PUNCT
ejpam-5611	288	18	δ(ξ	δ(ξ	NOUN
ejpam-5611	288	19	)	)	PUNCT
ejpam-5611	288	20	)	)	PUNCT
ejpam-5611	288	21	}	}	PUNCT
ejpam-5611	288	22	·	·	PUNCT
ejpam-5611	289	1	∫	∫	INTJ
ejpam-5611	290	1	i	i	PRON
ejpam-5611	290	2	φ	φ	PROPN
ejpam-5611	290	3	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5611	291	1	g.	g.	PROPN
ejpam-5611	291	2	flores	flores	PROPN
ejpam-5611	291	3	,	,	PUNCT
ejpam-5611	291	4	a.	a.	PROPN
ejpam-5611	291	5	flores	flores	PROPN
ejpam-5611	291	6	/	/	SYM
ejpam-5611	291	7	eur	eur	PROPN
ejpam-5611	291	8	.	.	PUNCT
ejpam-5611	292	1	j.	j.	PROPN
ejpam-5611	292	2	pure	pure	PROPN
ejpam-5611	292	3	appl	appl	PROPN
ejpam-5611	292	4	.	.	PROPN
ejpam-5611	292	5	math	math	PROPN
ejpam-5611	292	6	,	,	PUNCT
ejpam-5611	292	7	18	18	NUM
ejpam-5611	292	8	(	(	PUNCT
ejpam-5611	292	9	2	2	NUM
ejpam-5611	292	10	)	)	PUNCT
ejpam-5611	292	11	(	(	PUNCT
ejpam-5611	292	12	2025	2025	NUM
ejpam-5611	292	13	)	)	PUNCT
ejpam-5611	292	14	,	,	PUNCT
ejpam-5611	292	15	5611	5611	NUM
ejpam-5611	292	16	12	12	NUM
ejpam-5611	292	17	of	of	ADP
ejpam-5611	292	18	16	16	NUM
ejpam-5611	292	19	≤	≤	NOUN
ejpam-5611	292	20	∑	∑	PUNCT
ejpam-5611	292	21	d1	d1	PROPN
ejpam-5611	292	22	∥∥f(ξ)∥∥	∥∥f(ξ)∥∥	PROPN
ejpam-5611	292	23	·	·	PUNCT
ejpam-5611	292	24	sup	sup	PROPN
ejpam-5611	292	25	{	{	PUNCT
ejpam-5611	292	26	|ϕ(ξ)−	|ϕ(ξ)−	NOUN
ejpam-5611	292	27	ϕ(x)|	ϕ(x)|	VERB
ejpam-5611	292	28	:	:	PUNCT
ejpam-5611	292	29	x	x	SYM
ejpam-5611	292	30	∈	∈	PROPN
ejpam-5611	292	31	b(ξ	b(ξ	NOUN
ejpam-5611	292	32	,	,	PUNCT
ejpam-5611	292	33	δ(ξ	δ(ξ	NOUN
ejpam-5611	292	34	)	)	PUNCT
ejpam-5611	292	35	)	)	PUNCT
ejpam-5611	292	36	}	}	PUNCT
ejpam-5611	292	37	·	·	PUNCT
ejpam-5611	293	1	∫	∫	INTJ
ejpam-5611	293	2	i	i	PRON
ejpam-5611	293	3	φ	φ	VERB
ejpam-5611	293	4	≤	≤	PROPN
ejpam-5611	293	5	ϵ	ϵ	ADP
ejpam-5611	293	6	3(m	3(m	NUM
ejpam-5611	293	7	+	+	CCONJ
ejpam-5611	293	8	1	1	NUM
ejpam-5611	293	9	)	)	PUNCT
ejpam-5611	293	10	·	·	PUNCT
ejpam-5611	294	1	∑	∑	PUNCT
ejpam-5611	294	2	d1	d1	PROPN
ejpam-5611	294	3	∫	∫	PROPN
ejpam-5611	295	1	i	i	PRON
ejpam-5611	295	2	φ	φ	VERB
ejpam-5611	295	3	≤	≤	PROPN
ejpam-5611	295	4	ϵ	ϵ	ADP
ejpam-5611	295	5	3(m	3(m	NUM
ejpam-5611	296	1	+	+	CCONJ
ejpam-5611	296	2	1	1	NUM
ejpam-5611	296	3	)	)	PUNCT
ejpam-5611	296	4	·	·	PUNCT
ejpam-5611	297	1	(	(	PUNCT
ejpam-5611	297	2	m	m	VERB
ejpam-5611	297	3	+	+	ADJ
ejpam-5611	297	4	1	1	X
ejpam-5611	297	5	)	)	PUNCT
ejpam-5611	297	6	=	=	SYM
ejpam-5611	297	7	ϵ	ϵ	ADP
ejpam-5611	297	8	3	3	NUM
ejpam-5611	297	9	,	,	PUNCT
ejpam-5611	297	10	that	that	ADV
ejpam-5611	297	11	is	is	ADV
ejpam-5611	297	12	,	,	PUNCT
ejpam-5611	297	13	∥∥∥∥∑	∥∥∥∥∑	PROPN
ejpam-5611	297	14	d1	d1	PROPN
ejpam-5611	297	15	f(ξ)ϕ(ξ	f(ξ)ϕ(ξ	NOUN
ejpam-5611	297	16	)	)	PUNCT
ejpam-5611	297	17	∫	∫	PROPN
ejpam-5611	298	1	i	i	PRON
ejpam-5611	298	2	φ−	φ−	PROPN
ejpam-5611	298	3	∑	∑	ADV
ejpam-5611	298	4	d1	d1	PROPN
ejpam-5611	298	5	f(ξ	f(ξ	NOUN
ejpam-5611	298	6	)	)	PUNCT
ejpam-5611	298	7	∫	∫	PROPN
ejpam-5611	299	1	i	i	PRON
ejpam-5611	299	2	ϕ	ϕ	PROPN
ejpam-5611	299	3	·	·	PUNCT
ejpam-5611	299	4	φ	φ	PROPN
ejpam-5611	299	5	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5611	299	6	<	<	X
ejpam-5611	299	7	ϵ	ϵ	X
ejpam-5611	299	8	3	3	NUM
ejpam-5611	299	9	(	(	PUNCT
ejpam-5611	299	10	3.17	3.17	NUM
ejpam-5611	299	11	)	)	PUNCT
ejpam-5611	299	12	in	in	ADP
ejpam-5611	299	13	similar	similar	ADJ
ejpam-5611	299	14	fashion,∥∥∥∥∑	fashion,∥∥∥∥∑	PROPN
ejpam-5611	299	15	d2	d2	PROPN
ejpam-5611	299	16	f(η)ϕ(η	f(η)ϕ(η	ADV
ejpam-5611	299	17	)	)	PUNCT
ejpam-5611	299	18	∫	∫	PROPN
ejpam-5611	300	1	j	j	PROPN
ejpam-5611	300	2	ψ	ψ	PROPN
ejpam-5611	300	3	−	−	PROPN
ejpam-5611	300	4	∑	∑	PROPN
ejpam-5611	300	5	d2	d2	PROPN
ejpam-5611	300	6	f(η	f(η	PROPN
ejpam-5611	300	7	)	)	PUNCT
ejpam-5611	301	1	∫	∫	PROPN
ejpam-5611	301	2	j	j	PROPN
ejpam-5611	301	3	ϕ	ϕ	PROPN
ejpam-5611	301	4	·	·	PUNCT
ejpam-5611	301	5	ψ	ψ	X
ejpam-5611	301	6	∥∥∥∥	∥∥∥∥	NUM
ejpam-5611	301	7	=	=	SYM
ejpam-5611	301	8	∥∥∥∥∑	∥∥∥∥∑	PROPN
ejpam-5611	301	9	d2	d2	PROPN
ejpam-5611	301	10	f(η	f(η	PROPN
ejpam-5611	301	11	)	)	PUNCT
ejpam-5611	301	12	∫	∫	PROPN
ejpam-5611	301	13	j	j	PROPN
ejpam-5611	301	14	ϕ(η	ϕ(η	PROPN
ejpam-5611	301	15	)	)	PUNCT
ejpam-5611	301	16	·	·	PUNCT
ejpam-5611	302	1	ψ	ψ	X
ejpam-5611	302	2	−	−	PRON
ejpam-5611	302	3	∑	∑	PROPN
ejpam-5611	302	4	d2	d2	PROPN
ejpam-5611	302	5	f(η	f(η	PROPN
ejpam-5611	302	6	)	)	PUNCT
ejpam-5611	302	7	∫	∫	PROPN
ejpam-5611	303	1	j	j	PROPN
ejpam-5611	303	2	ϕ	ϕ	PROPN
ejpam-5611	303	3	·	·	PUNCT
ejpam-5611	303	4	ψ	ψ	X
ejpam-5611	303	5	∥∥∥∥	∥∥∥∥	NUM
ejpam-5611	303	6	=	=	SYM
ejpam-5611	303	7	∥∥∥∥∑	∥∥∥∥∑	PROPN
ejpam-5611	303	8	d2	d2	PROPN
ejpam-5611	303	9	f(η	f(η	PROPN
ejpam-5611	303	10	)	)	PUNCT
ejpam-5611	304	1	[	[	PUNCT
ejpam-5611	304	2	∫	∫	PROPN
ejpam-5611	304	3	j	j	PROPN
ejpam-5611	304	4	ϕ(η	ϕ(η	PROPN
ejpam-5611	304	5	)	)	PUNCT
ejpam-5611	304	6	·	·	PUNCT
ejpam-5611	305	1	ψ	ψ	X
ejpam-5611	306	1	−	−	NOUN
ejpam-5611	306	2	∫	∫	PROPN
ejpam-5611	306	3	j	j	PROPN
ejpam-5611	306	4	ϕ	ϕ	X
ejpam-5611	306	5	·	·	PUNCT
ejpam-5611	306	6	ψ	ψ	X
ejpam-5611	306	7	]	]	X
ejpam-5611	306	8	∥∥∥∥	∥∥∥∥	NUM
ejpam-5611	306	9	=	=	SYM
ejpam-5611	306	10	∥∥∥∥∑	∥∥∥∥∑	PROPN
ejpam-5611	306	11	d2	d2	PROPN
ejpam-5611	306	12	f(η	f(η	PROPN
ejpam-5611	306	13	)	)	PUNCT
ejpam-5611	306	14	[	[	PUNCT
ejpam-5611	306	15	∫	∫	PROPN
ejpam-5611	306	16	j	j	PROPN
ejpam-5611	306	17	(	(	PUNCT
ejpam-5611	306	18	ϕ(η	ϕ(η	PROPN
ejpam-5611	306	19	)	)	PUNCT
ejpam-5611	306	20	·	·	PUNCT
ejpam-5611	307	1	ψ	ψ	X
ejpam-5611	307	2	−	−	X
ejpam-5611	307	3	ϕ	ϕ	X
ejpam-5611	307	4	·	·	PUNCT
ejpam-5611	307	5	ψ	ψ	NOUN
ejpam-5611	307	6	)	)	PUNCT
ejpam-5611	307	7	]	]	PUNCT
ejpam-5611	307	8	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-5611	307	9	=	=	SYM
ejpam-5611	307	10	∥∥∥∥∑	∥∥∥∥∑	PROPN
ejpam-5611	307	11	d2	d2	PROPN
ejpam-5611	307	12	f(η	f(η	PROPN
ejpam-5611	307	13	)	)	PUNCT
ejpam-5611	307	14	[	[	PUNCT
ejpam-5611	307	15	∫	∫	PROPN
ejpam-5611	307	16	j	j	PROPN
ejpam-5611	307	17	(	(	PUNCT
ejpam-5611	307	18	ϕ(η)−	ϕ(η)−	NOUN
ejpam-5611	307	19	ϕ	ϕ	PROPN
ejpam-5611	307	20	)	)	PUNCT
ejpam-5611	307	21	·	·	PUNCT
ejpam-5611	308	1	ψ	ψ	X
ejpam-5611	308	2	]	]	X
ejpam-5611	308	3	∥∥∥∥	∥∥∥∥	NUM
ejpam-5611	308	4	≤	≤	NUM
ejpam-5611	308	5	∥∥∥∥∑	∥∥∥∥∑	PROPN
ejpam-5611	308	6	d2	d2	PROPN
ejpam-5611	308	7	f(η	f(η	PROPN
ejpam-5611	308	8	)	)	PUNCT
ejpam-5611	308	9	·	·	PUNCT
ejpam-5611	309	1	∫	∫	PROPN
ejpam-5611	309	2	j	j	PROPN
ejpam-5611	309	3	sup	sup	PROPN
ejpam-5611	309	4	{	{	PUNCT
ejpam-5611	309	5	|ϕ(η)−	|ϕ(η)−	NOUN
ejpam-5611	309	6	ϕ(x)|	ϕ(x)|	VERB
ejpam-5611	309	7	:	:	PUNCT
ejpam-5611	309	8	x	x	SYM
ejpam-5611	309	9	∈	∈	PROPN
ejpam-5611	309	10	b(η	b(η	NOUN
ejpam-5611	309	11	,	,	PUNCT
ejpam-5611	309	12	δ(η	δ(η	PROPN
ejpam-5611	309	13	)	)	PUNCT
ejpam-5611	309	14	)	)	PUNCT
ejpam-5611	309	15	}	}	PUNCT
ejpam-5611	309	16	·	·	PUNCT
ejpam-5611	310	1	ψ	ψ	X
ejpam-5611	310	2	∥∥∥∥	∥∥∥∥	ADJ
ejpam-5611	310	3	≤	≤	NUM
ejpam-5611	310	4	∥∥∥∥∑	∥∥∥∥∑	PROPN
ejpam-5611	310	5	d2	d2	PROPN
ejpam-5611	310	6	f(η	f(η	PROPN
ejpam-5611	310	7	)	)	PUNCT
ejpam-5611	310	8	·	·	PUNCT
ejpam-5611	310	9	sup	sup	NOUN
ejpam-5611	310	10	{	{	PUNCT
ejpam-5611	310	11	|ϕ(η)−	|ϕ(η)−	NOUN
ejpam-5611	310	12	ϕ(x)|	ϕ(x)|	VERB
ejpam-5611	310	13	:	:	PUNCT
ejpam-5611	310	14	x	x	SYM
ejpam-5611	310	15	∈	∈	PROPN
ejpam-5611	310	16	b(η	b(η	NOUN
ejpam-5611	310	17	,	,	PUNCT
ejpam-5611	310	18	δ(η	δ(η	PROPN
ejpam-5611	310	19	)	)	PUNCT
ejpam-5611	310	20	)	)	PUNCT
ejpam-5611	310	21	}	}	PUNCT
ejpam-5611	310	22	·	·	PUNCT
ejpam-5611	311	1	∫	∫	PROPN
ejpam-5611	311	2	j	j	PROPN
ejpam-5611	311	3	ψ	ψ	PROPN
ejpam-5611	311	4	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5611	311	5	≤	≤	NUM
ejpam-5611	311	6	∑	∑	PUNCT
ejpam-5611	311	7	d2	d2	PROPN
ejpam-5611	311	8	∥∥f(η)∥∥	∥∥f(η)∥∥	X
ejpam-5611	311	9	·	·	PUNCT
ejpam-5611	311	10	sup	sup	NOUN
ejpam-5611	311	11	{	{	PUNCT
ejpam-5611	311	12	|ϕ(η)−	|ϕ(η)−	NOUN
ejpam-5611	311	13	ϕ(x)|	ϕ(x)|	VERB
ejpam-5611	311	14	:	:	PUNCT
ejpam-5611	311	15	x	x	SYM
ejpam-5611	311	16	∈	∈	PROPN
ejpam-5611	311	17	b(η	b(η	NOUN
ejpam-5611	311	18	,	,	PUNCT
ejpam-5611	311	19	δ(η	δ(η	PROPN
ejpam-5611	311	20	)	)	PUNCT
ejpam-5611	311	21	)	)	PUNCT
ejpam-5611	311	22	}	}	PUNCT
ejpam-5611	311	23	·	·	PUNCT
ejpam-5611	312	1	∫	∫	PROPN
ejpam-5611	312	2	j	j	PROPN
ejpam-5611	312	3	ψ	ψ	X
ejpam-5611	312	4	≤	≤	NUM
ejpam-5611	312	5	ϵ	ϵ	ADP
ejpam-5611	312	6	3	3	NUM
ejpam-5611	312	7	(	(	PUNCT
ejpam-5611	312	8	m	m	VERB
ejpam-5611	312	9	+	+	ADJ
ejpam-5611	312	10	1	1	NUM
ejpam-5611	312	11	)	)	PUNCT
ejpam-5611	312	12	·	·	PUNCT
ejpam-5611	312	13	∑	∑	PUNCT
ejpam-5611	312	14	d2	d2	PROPN
ejpam-5611	312	15	∫	∫	PROPN
ejpam-5611	312	16	j	j	PROPN
ejpam-5611	312	17	ψ	ψ	PROPN
ejpam-5611	312	18	≤	≤	NUM
ejpam-5611	312	19	ϵ	ϵ	ADP
ejpam-5611	312	20	3	3	NUM
ejpam-5611	312	21	(	(	PUNCT
ejpam-5611	312	22	m	m	VERB
ejpam-5611	312	23	+	+	ADJ
ejpam-5611	312	24	1	1	NUM
ejpam-5611	312	25	)	)	PUNCT
ejpam-5611	312	26	·	·	PUNCT
ejpam-5611	313	1	(	(	PUNCT
ejpam-5611	313	2	m	m	VERB
ejpam-5611	313	3	+	+	ADJ
ejpam-5611	313	4	1	1	X
ejpam-5611	313	5	)	)	PUNCT
ejpam-5611	313	6	=	=	SYM
ejpam-5611	313	7	ϵ	ϵ	ADP
ejpam-5611	313	8	3	3	NUM
ejpam-5611	313	9	,	,	PUNCT
ejpam-5611	313	10	in	in	ADP
ejpam-5611	313	11	other	other	ADJ
ejpam-5611	313	12	words	word	NOUN
ejpam-5611	313	13	,	,	PUNCT
ejpam-5611	313	14	∥∥∥∥∑	∥∥∥∥∑	PROPN
ejpam-5611	313	15	d2	d2	PROPN
ejpam-5611	313	16	f(η)ϕ(η	f(η)ϕ(η	ADV
ejpam-5611	313	17	)	)	PUNCT
ejpam-5611	314	1	∫	∫	PROPN
ejpam-5611	314	2	j	j	PROPN
ejpam-5611	314	3	ψ	ψ	PROPN
ejpam-5611	314	4	−	−	PROPN
ejpam-5611	314	5	∑	∑	PROPN
ejpam-5611	314	6	d2	d2	PROPN
ejpam-5611	314	7	f(η	f(η	PROPN
ejpam-5611	314	8	)	)	PUNCT
ejpam-5611	314	9	∫	∫	PROPN
ejpam-5611	315	1	j	j	PROPN
ejpam-5611	315	2	ϕ	ϕ	PROPN
ejpam-5611	315	3	·	·	PUNCT
ejpam-5611	315	4	ψ	ψ	ADP
ejpam-5611	315	5	∥∥∥∥	∥∥∥∥	NOUN
ejpam-5611	315	6	<	<	X
ejpam-5611	315	7	ϵ	ϵ	X
ejpam-5611	315	8	3	3	NUM
ejpam-5611	315	9	(	(	PUNCT
ejpam-5611	315	10	3.18	3.18	NUM
ejpam-5611	315	11	)	)	PUNCT
ejpam-5611	315	12	therefore	therefore	ADV
ejpam-5611	315	13	,	,	PUNCT
ejpam-5611	315	14	by	by	ADP
ejpam-5611	315	15	(	(	PUNCT
ejpam-5611	315	16	3.16	3.16	NUM
ejpam-5611	315	17	)	)	PUNCT
ejpam-5611	315	18	,	,	PUNCT
ejpam-5611	315	19	(	(	PUNCT
ejpam-5611	315	20	3.17	3.17	NUM
ejpam-5611	315	21	)	)	PUNCT
ejpam-5611	315	22	,	,	PUNCT
ejpam-5611	315	23	and	and	CCONJ
ejpam-5611	315	24	(	(	PUNCT
ejpam-5611	315	25	3.18)∥∥∥∥∑	3.18)∥∥∥∥∑	NUM
ejpam-5611	315	26	d1	d1	PROPN
ejpam-5611	315	27	f(ξ)ϕ(ξ	f(ξ)ϕ(ξ	NOUN
ejpam-5611	315	28	)	)	PUNCT
ejpam-5611	315	29	∫	∫	PROPN
ejpam-5611	316	1	i	i	PRON
ejpam-5611	316	2	φ−	φ−	PROPN
ejpam-5611	316	3	∑	∑	PUNCT
ejpam-5611	316	4	d2	d2	PROPN
ejpam-5611	316	5	f(η)ϕ(η	f(η)ϕ(η	ADV
ejpam-5611	316	6	)	)	PUNCT
ejpam-5611	316	7	∫	∫	PROPN
ejpam-5611	317	1	i	i	PRON
ejpam-5611	317	2	ψ	ψ	PROPN
ejpam-5611	317	3	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5611	317	4	g.	g.	PROPN
ejpam-5611	317	5	flores	flores	PROPN
ejpam-5611	317	6	,	,	PUNCT
ejpam-5611	317	7	a.	a.	PROPN
ejpam-5611	317	8	flores	flores	PROPN
ejpam-5611	317	9	/	/	SYM
ejpam-5611	317	10	eur	eur	PROPN
ejpam-5611	317	11	.	.	PUNCT
ejpam-5611	318	1	j.	j.	PROPN
ejpam-5611	318	2	pure	pure	PROPN
ejpam-5611	318	3	appl	appl	PROPN
ejpam-5611	318	4	.	.	PROPN
ejpam-5611	318	5	math	math	PROPN
ejpam-5611	318	6	,	,	PUNCT
ejpam-5611	318	7	18	18	NUM
ejpam-5611	318	8	(	(	PUNCT
ejpam-5611	318	9	2	2	NUM
ejpam-5611	318	10	)	)	PUNCT
ejpam-5611	318	11	(	(	PUNCT
ejpam-5611	318	12	2025	2025	NUM
ejpam-5611	318	13	)	)	PUNCT
ejpam-5611	318	14	,	,	PUNCT
ejpam-5611	318	15	5611	5611	NUM
ejpam-5611	318	16	13	13	NUM
ejpam-5611	318	17	of	of	ADP
ejpam-5611	318	18	16	16	NUM
ejpam-5611	318	19	=	=	SYM
ejpam-5611	318	20	∥∥∥∥∑	∥∥∥∥∑	PROPN
ejpam-5611	318	21	d1	d1	PROPN
ejpam-5611	318	22	f(ξ)ϕ(ξ	f(ξ)ϕ(ξ	NOUN
ejpam-5611	318	23	)	)	PUNCT
ejpam-5611	318	24	∫	∫	PROPN
ejpam-5611	319	1	i	i	PRON
ejpam-5611	319	2	φ−	φ−	PROPN
ejpam-5611	319	3	∑	∑	ADV
ejpam-5611	319	4	d1	d1	PROPN
ejpam-5611	319	5	f(ξ	f(ξ	NOUN
ejpam-5611	319	6	)	)	PUNCT
ejpam-5611	319	7	∫	∫	PROPN
ejpam-5611	320	1	i	i	PRON
ejpam-5611	320	2	ϕ	ϕ	X
ejpam-5611	320	3	·	·	PUNCT
ejpam-5611	320	4	φ+	φ+	X
ejpam-5611	320	5	∑	∑	PUNCT
ejpam-5611	320	6	d1	d1	PROPN
ejpam-5611	320	7	f(ξ	f(ξ	NOUN
ejpam-5611	320	8	)	)	PUNCT
ejpam-5611	320	9	∫	∫	PROPN
ejpam-5611	321	1	i	i	PRON
ejpam-5611	321	2	ϕ	ϕ	PROPN
ejpam-5611	321	3	·	·	PUNCT
ejpam-5611	321	4	φ	φ	NUM
ejpam-5611	321	5	−	−	PROPN
ejpam-5611	321	6	∑	∑	PROPN
ejpam-5611	321	7	d2	d2	PROPN
ejpam-5611	321	8	f(η	f(η	PROPN
ejpam-5611	321	9	)	)	PUNCT
ejpam-5611	322	1	∫	∫	PROPN
ejpam-5611	323	1	j	j	PROPN
ejpam-5611	323	2	ϕ	ϕ	X
ejpam-5611	323	3	·	·	PUNCT
ejpam-5611	323	4	ψ	ψ	X
ejpam-5611	323	5	+	+	CCONJ
ejpam-5611	323	6	∑	∑	PROPN
ejpam-5611	323	7	d2	d2	PROPN
ejpam-5611	323	8	f(η	f(η	PROPN
ejpam-5611	323	9	)	)	PUNCT
ejpam-5611	324	1	∫	∫	PROPN
ejpam-5611	324	2	j	j	PROPN
ejpam-5611	324	3	ϕ	ϕ	X
ejpam-5611	324	4	·	·	PUNCT
ejpam-5611	324	5	ψ	ψ	X
ejpam-5611	324	6	−	−	PRON
ejpam-5611	324	7	∑	∑	PUNCT
ejpam-5611	324	8	d2	d2	PROPN
ejpam-5611	324	9	f(η)ϕ(η	f(η)ϕ(η	ADV
ejpam-5611	324	10	)	)	PUNCT
ejpam-5611	324	11	∫	∫	PROPN
ejpam-5611	325	1	j	j	PROPN
ejpam-5611	325	2	ψ	ψ	PROPN
ejpam-5611	325	3	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5611	325	4	≤	≤	NUM
ejpam-5611	325	5	∥∥∥∥∑	∥∥∥∥∑	PROPN
ejpam-5611	325	6	d1	d1	PROPN
ejpam-5611	325	7	f(ξ)ϕ(ξ	f(ξ)ϕ(ξ	NOUN
ejpam-5611	325	8	)	)	PUNCT
ejpam-5611	325	9	∫	∫	PROPN
ejpam-5611	326	1	i	i	PRON
ejpam-5611	326	2	φ−	φ−	PROPN
ejpam-5611	326	3	∑	∑	ADV
ejpam-5611	326	4	d1	d1	PROPN
ejpam-5611	326	5	f(ξ	f(ξ	NOUN
ejpam-5611	326	6	)	)	PUNCT
ejpam-5611	326	7	∫	∫	PROPN
ejpam-5611	327	1	i	i	PRON
ejpam-5611	327	2	ϕ	ϕ	PROPN
ejpam-5611	327	3	·	·	PUNCT
ejpam-5611	327	4	φ	φ	NUM
ejpam-5611	327	5	∥∥∥∥	∥∥∥∥	NUM
ejpam-5611	328	1	+	+	CCONJ
ejpam-5611	328	2	∥∥∥∥∑	∥∥∥∥∑	PROPN
ejpam-5611	328	3	d1	d1	PROPN
ejpam-5611	328	4	f(ξ	f(ξ	NOUN
ejpam-5611	328	5	)	)	PUNCT
ejpam-5611	328	6	∫	∫	PROPN
ejpam-5611	329	1	i	i	PRON
ejpam-5611	329	2	ϕ	ϕ	PROPN
ejpam-5611	329	3	·	·	PUNCT
ejpam-5611	329	4	φ−	φ−	PROPN
ejpam-5611	329	5	∑	∑	PUNCT
ejpam-5611	329	6	d2	d2	PROPN
ejpam-5611	329	7	f(η	f(η	PROPN
ejpam-5611	329	8	)	)	PUNCT
ejpam-5611	330	1	∫	∫	PROPN
ejpam-5611	330	2	j	j	PROPN
ejpam-5611	330	3	ϕ	ϕ	X
ejpam-5611	330	4	·	·	PUNCT
ejpam-5611	330	5	ψ	ψ	ADP
ejpam-5611	330	6	∥∥∥∥	∥∥∥∥	NUM
ejpam-5611	330	7	+	+	CCONJ
ejpam-5611	330	8	∥∥∥∥∑	∥∥∥∥∑	PROPN
ejpam-5611	330	9	d2	d2	PROPN
ejpam-5611	330	10	f(η	f(η	PROPN
ejpam-5611	330	11	)	)	PUNCT
ejpam-5611	330	12	∫	∫	PROPN
ejpam-5611	331	1	j	j	PROPN
ejpam-5611	331	2	ϕ	ϕ	X
ejpam-5611	331	3	·	·	PUNCT
ejpam-5611	331	4	ψ	ψ	X
ejpam-5611	331	5	−	−	PRON
ejpam-5611	331	6	∑	∑	PUNCT
ejpam-5611	331	7	d2	d2	PROPN
ejpam-5611	331	8	f(η)ϕ(η	f(η)ϕ(η	ADV
ejpam-5611	331	9	)	)	PUNCT
ejpam-5611	331	10	∫	∫	PROPN
ejpam-5611	331	11	j	j	PROPN
ejpam-5611	331	12	ψ	ψ	PROPN
ejpam-5611	331	13	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5611	331	14	<	<	X
ejpam-5611	331	15	ϵ	ϵ	X
ejpam-5611	331	16	3	3	NUM
ejpam-5611	331	17	+	+	CCONJ
ejpam-5611	331	18	ϵ	ϵ	SYM
ejpam-5611	331	19	3	3	NUM
ejpam-5611	331	20	+	+	CCONJ
ejpam-5611	331	21	ϵ	ϵ	SYM
ejpam-5611	331	22	3	3	NUM
ejpam-5611	331	23	=	=	SYM
ejpam-5611	331	24	ϵ.	ϵ.	NOUN
ejpam-5611	331	25	and	and	CCONJ
ejpam-5611	331	26	the	the	DET
ejpam-5611	331	27	result	result	NOUN
ejpam-5611	331	28	follows	follow	VERB
ejpam-5611	331	29	.	.	PUNCT
ejpam-5611	332	1	□	□	PUNCT
ejpam-5611	332	2	we	we	PRON
ejpam-5611	332	3	now	now	ADV
ejpam-5611	332	4	show	show	VERB
ejpam-5611	332	5	a	a	DET
ejpam-5611	332	6	version	version	NOUN
ejpam-5611	332	7	of	of	ADP
ejpam-5611	332	8	the	the	DET
ejpam-5611	332	9	saks	sak	NOUN
ejpam-5611	332	10	-	-	PUNCT
ejpam-5611	332	11	henstock	henstock	NOUN
ejpam-5611	332	12	lemma	lemma	PROPN
ejpam-5611	332	13	for	for	ADP
ejpam-5611	332	14	the	the	DET
ejpam-5611	332	15	pu	pu	PROPN
ejpam-5611	332	16	integral	integral	PROPN
ejpam-5611	332	17	.	.	PUNCT
ejpam-5611	333	1	theorem	theorem	NOUN
ejpam-5611	333	2	2	2	NUM
ejpam-5611	333	3	.	.	PUNCT
ejpam-5611	333	4	(	(	PUNCT
ejpam-5611	333	5	saks	sak	NOUN
ejpam-5611	333	6	-	-	PUNCT
ejpam-5611	333	7	henstock	henstock	NOUN
ejpam-5611	333	8	lemma	lemma	PROPN
ejpam-5611	333	9	)	)	PUNCT
ejpam-5611	334	1	if	if	SCONJ
ejpam-5611	334	2	f	f	X
ejpam-5611	334	3	:	:	PUNCT
ejpam-5611	335	1	[	[	X
ejpam-5611	335	2	a	a	X
ejpam-5611	335	3	,	,	PUNCT
ejpam-5611	335	4	b	b	NOUN
ejpam-5611	335	5	]	]	X
ejpam-5611	335	6	→	→	PUNCT
ejpam-5611	335	7	x	x	X
ejpam-5611	335	8	is	be	AUX
ejpam-5611	335	9	pu	pu	PROPN
ejpam-5611	335	10	integrable	integrable	ADJ
ejpam-5611	335	11	over	over	ADP
ejpam-5611	335	12	[	[	X
ejpam-5611	335	13	a	a	DET
ejpam-5611	335	14	,	,	PUNCT
ejpam-5611	335	15	b	b	NOUN
ejpam-5611	335	16	]	]	X
ejpam-5611	335	17	,	,	PUNCT
ejpam-5611	335	18	then	then	ADV
ejpam-5611	335	19	for	for	ADP
ejpam-5611	335	20	every	every	DET
ejpam-5611	335	21	ϵ	ϵ	PROPN
ejpam-5611	335	22	>	>	X
ejpam-5611	335	23	0	0	NUM
ejpam-5611	335	24	,	,	PUNCT
ejpam-5611	335	25	there	there	PRON
ejpam-5611	335	26	exists	exist	VERB
ejpam-5611	335	27	a	a	DET
ejpam-5611	335	28	gauge	gauge	NOUN
ejpam-5611	335	29	δ	δ	NOUN
ejpam-5611	335	30	on	on	ADP
ejpam-5611	335	31	[	[	X
ejpam-5611	335	32	a	a	DET
ejpam-5611	335	33	,	,	PUNCT
ejpam-5611	335	34	b	b	NOUN
ejpam-5611	335	35	]	]	X
ejpam-5611	335	36	such	such	ADJ
ejpam-5611	335	37	that	that	PRON
ejpam-5611	335	38	for	for	ADP
ejpam-5611	335	39	any	any	DET
ejpam-5611	335	40	δ	δ	NOUN
ejpam-5611	335	41	-	-	PUNCT
ejpam-5611	335	42	fine	fine	ADJ
ejpam-5611	335	43	partial	partial	ADJ
ejpam-5611	335	44	division	division	NOUN
ejpam-5611	335	45	p	p	NOUN
ejpam-5611	335	46	=	=	PUNCT
ejpam-5611	335	47	{	{	PUNCT
ejpam-5611	335	48	(	(	PUNCT
ejpam-5611	335	49	ξ	ξ	PROPN
ejpam-5611	335	50	,	,	PUNCT
ejpam-5611	335	51	φ	φ	PROPN
ejpam-5611	335	52	,	,	PUNCT
ejpam-5611	335	53	i	i	NOUN
ejpam-5611	335	54	)	)	PUNCT
ejpam-5611	335	55	}	}	PUNCT
ejpam-5611	335	56	of	of	ADP
ejpam-5611	335	57	[	[	X
ejpam-5611	335	58	a	a	X
ejpam-5611	335	59	,	,	PUNCT
ejpam-5611	335	60	b	b	NOUN
ejpam-5611	335	61	]	]	X
ejpam-5611	335	62	,	,	PUNCT
ejpam-5611	335	63	we	we	PRON
ejpam-5611	335	64	have∥∥∥∥∥∑	have∥∥∥∥∥∑	VERB
ejpam-5611	335	65	p	p	NOUN
ejpam-5611	335	66	(	(	PUNCT
ejpam-5611	335	67	f(ξ	f(ξ	PROPN
ejpam-5611	335	68	)	)	PUNCT
ejpam-5611	335	69	∫	∫	NOUN
ejpam-5611	336	1	i	i	PRON
ejpam-5611	336	2	φ−	φ−	PROPN
ejpam-5611	336	3	(	(	PUNCT
ejpam-5611	336	4	p	p	NOUN
ejpam-5611	336	5	)	)	PUNCT
ejpam-5611	336	6	∫	∫	PROPN
ejpam-5611	337	1	i	i	PRON
ejpam-5611	337	2	fφ	fφ	VERB
ejpam-5611	337	3	)	)	PUNCT
ejpam-5611	337	4	∥∥∥∥∥	∥∥∥∥∥	X
ejpam-5611	337	5	<	<	X
ejpam-5611	337	6	ϵ.	ϵ.	NOUN
ejpam-5611	337	7	proof	proof	NOUN
ejpam-5611	337	8	:	:	PUNCT
ejpam-5611	337	9	fix	fix	VERB
ejpam-5611	337	10	ϵ	ϵ	X
ejpam-5611	337	11	>	>	X
ejpam-5611	337	12	0	0	NUM
ejpam-5611	337	13	.	.	PUNCT
ejpam-5611	338	1	then	then	ADV
ejpam-5611	338	2	choose	choose	VERB
ejpam-5611	338	3	a	a	DET
ejpam-5611	338	4	gauge	gauge	ADJ
ejpam-5611	338	5	δ	δ	NOUN
ejpam-5611	338	6	on	on	ADP
ejpam-5611	338	7	[	[	X
ejpam-5611	338	8	a	a	DET
ejpam-5611	338	9	,	,	PUNCT
ejpam-5611	338	10	b	b	NOUN
ejpam-5611	338	11	]	]	X
ejpam-5611	338	12	such	such	ADJ
ejpam-5611	338	13	that	that	SCONJ
ejpam-5611	338	14	whenever	whenever	SCONJ
ejpam-5611	338	15	d	d	NOUN
ejpam-5611	338	16	=	=	SYM
ejpam-5611	338	17	{	{	PUNCT
ejpam-5611	338	18	(	(	PUNCT
ejpam-5611	338	19	ξ	ξ	PROPN
ejpam-5611	338	20	,	,	PUNCT
ejpam-5611	338	21	σ	σ	PROPN
ejpam-5611	338	22	,	,	PUNCT
ejpam-5611	338	23	i	i	NOUN
ejpam-5611	338	24	)	)	PUNCT
ejpam-5611	338	25	}	}	PUNCT
ejpam-5611	338	26	is	be	AUX
ejpam-5611	338	27	a	a	DET
ejpam-5611	338	28	δ	δ	NOUN
ejpam-5611	338	29	-	-	PUNCT
ejpam-5611	338	30	fine	fine	ADJ
ejpam-5611	338	31	division	division	NOUN
ejpam-5611	338	32	of	of	ADP
ejpam-5611	338	33	[	[	X
ejpam-5611	338	34	a	a	X
ejpam-5611	338	35	,	,	PUNCT
ejpam-5611	338	36	b	b	NOUN
ejpam-5611	338	37	]	]	X
ejpam-5611	338	38	,	,	PUNCT
ejpam-5611	338	39	we	we	PRON
ejpam-5611	338	40	have∥∥∥∥∑	have∥∥∥∥∑	PUNCT
ejpam-5611	338	41	d	d	ADJ
ejpam-5611	338	42	f(ξ	f(ξ	NOUN
ejpam-5611	338	43	)	)	PUNCT
ejpam-5611	338	44	∫	∫	PROPN
ejpam-5611	339	1	i	i	PROPN
ejpam-5611	339	2	σ	σ	NOUN
ejpam-5611	339	3	−	−	PROPN
ejpam-5611	339	4	(	(	PUNCT
ejpam-5611	339	5	p	p	NOUN
ejpam-5611	339	6	)	)	PUNCT
ejpam-5611	339	7	∫	∫	PROPN
ejpam-5611	340	1	[	[	X
ejpam-5611	340	2	a	a	X
ejpam-5611	340	3	,	,	PUNCT
ejpam-5611	340	4	b	b	NOUN
ejpam-5611	340	5	]	]	X
ejpam-5611	340	6	f	f	X
ejpam-5611	340	7	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5611	340	8	<	<	X
ejpam-5611	340	9	ϵ.	ϵ.	NOUN
ejpam-5611	340	10	let	let	VERB
ejpam-5611	340	11	p	p	NOUN
ejpam-5611	340	12	=	=	PRON
ejpam-5611	340	13	{	{	PUNCT
ejpam-5611	340	14	(	(	PUNCT
ejpam-5611	340	15	ξ	ξ	PROPN
ejpam-5611	340	16	,	,	PUNCT
ejpam-5611	340	17	φ	φ	PROPN
ejpam-5611	340	18	,	,	PUNCT
ejpam-5611	340	19	i	i	NOUN
ejpam-5611	340	20	)	)	PUNCT
ejpam-5611	340	21	}	}	PUNCT
ejpam-5611	340	22	be	be	AUX
ejpam-5611	340	23	a	a	DET
ejpam-5611	340	24	δ	δ	NOUN
ejpam-5611	340	25	-	-	PUNCT
ejpam-5611	340	26	fine	fine	ADJ
ejpam-5611	340	27	partial	partial	ADJ
ejpam-5611	340	28	division	division	NOUN
ejpam-5611	340	29	of	of	ADP
ejpam-5611	340	30	[	[	X
ejpam-5611	340	31	a	a	X
ejpam-5611	340	32	,	,	PUNCT
ejpam-5611	340	33	b	b	NOUN
ejpam-5611	340	34	]	]	PUNCT
ejpam-5611	340	35	and	and	CCONJ
ejpam-5611	340	36	put	put	VERB
ejpam-5611	340	37	ϕ	ϕ	NOUN
ejpam-5611	340	38	=	=	PUNCT
ejpam-5611	340	39	∑	∑	PUNCT
ejpam-5611	340	40	p	p	X
ejpam-5611	340	41	φ	φ	NOUN
ejpam-5611	340	42	.	.	PUNCT
ejpam-5611	341	1	we	we	PRON
ejpam-5611	341	2	choose	choose	VERB
ejpam-5611	341	3	a	a	DET
ejpam-5611	341	4	δ1(x	δ1(x	NOUN
ejpam-5611	341	5	)	)	PUNCT
ejpam-5611	341	6	≤	≤	NOUN
ejpam-5611	341	7	δ(x	δ(x	NOUN
ejpam-5611	341	8	)	)	PUNCT
ejpam-5611	341	9	such	such	ADJ
ejpam-5611	341	10	that	that	PRON
ejpam-5611	341	11	for	for	ADP
ejpam-5611	341	12	any	any	DET
ejpam-5611	341	13	y	y	PROPN
ejpam-5611	341	14	∈	∈	PROPN
ejpam-5611	341	15	[	[	X
ejpam-5611	341	16	a	a	X
ejpam-5611	341	17	,	,	PUNCT
ejpam-5611	341	18	b	b	NOUN
ejpam-5611	341	19	]	]	X
ejpam-5611	341	20	∩b(x	∩b(x	ADJ
ejpam-5611	341	21	,	,	PUNCT
ejpam-5611	341	22	δ1(x	δ1(x	PROPN
ejpam-5611	341	23	)	)	PUNCT
ejpam-5611	341	24	)	)	PUNCT
ejpam-5611	341	25	,	,	PUNCT
ejpam-5611	341	26	we	we	PRON
ejpam-5611	341	27	have	have	VERB
ejpam-5611	341	28	∥f(x)∥|ϕ(y)−	∥f(x)∥|ϕ(y)−	PROPN
ejpam-5611	341	29	ϕ(x)|	ϕ(x)|	PROPN
ejpam-5611	341	30	<	<	X
ejpam-5611	341	31	ϵ	ϵ	X
ejpam-5611	341	32	3	3	NUM
ejpam-5611	341	33	.	.	PUNCT
ejpam-5611	342	1	so	so	ADV
ejpam-5611	342	2	,	,	PUNCT
ejpam-5611	342	3	for	for	ADP
ejpam-5611	342	4	each	each	DET
ejpam-5611	342	5	x	x	SYM
ejpam-5611	342	6	∈	∈	PROPN
ejpam-5611	342	7	supp	supp	NOUN
ejpam-5611	342	8	f	f	PROPN
ejpam-5611	342	9	∥f(x)∥	∥f(x)∥	PROPN
ejpam-5611	342	10	·	·	PUNCT
ejpam-5611	342	11	sup	sup	NOUN
ejpam-5611	342	12	{	{	PUNCT
ejpam-5611	342	13	|ϕ(x)−	|ϕ(x)−	NOUN
ejpam-5611	342	14	ϕ(y)|	ϕ(y)|	NOUN
ejpam-5611	342	15	:	:	PUNCT
ejpam-5611	342	16	y	y	PROPN
ejpam-5611	342	17	∈	∈	PROPN
ejpam-5611	342	18	b(x	b(x	NOUN
ejpam-5611	342	19	,	,	PUNCT
ejpam-5611	342	20	δ1(x	δ1(x	NOUN
ejpam-5611	342	21	)	)	PUNCT
ejpam-5611	342	22	)	)	PUNCT
ejpam-5611	342	23	}	}	PUNCT
ejpam-5611	342	24	<	<	X
ejpam-5611	342	25	ϵ	ϵ	X
ejpam-5611	342	26	3	3	NUM
ejpam-5611	342	27	.	.	PUNCT
ejpam-5611	343	1	(	(	PUNCT
ejpam-5611	343	2	3.19	3.19	NUM
ejpam-5611	343	3	)	)	PUNCT
ejpam-5611	343	4	now	now	ADV
ejpam-5611	343	5	,	,	PUNCT
ejpam-5611	343	6	by	by	ADP
ejpam-5611	343	7	lemma	lemma	PROPN
ejpam-5611	343	8	3	3	NUM
ejpam-5611	343	9	,	,	PUNCT
ejpam-5611	343	10	f	f	PROPN
ejpam-5611	343	11	·	·	PUNCT
ejpam-5611	343	12	(	(	PUNCT
ejpam-5611	343	13	1−	1−	NUM
ejpam-5611	343	14	ϕ	ϕ	NOUN
ejpam-5611	343	15	)	)	PUNCT
ejpam-5611	343	16	is	be	AUX
ejpam-5611	343	17	pu	pu	PROPN
ejpam-5611	343	18	integrable	integrable	ADJ
ejpam-5611	343	19	over	over	ADP
ejpam-5611	343	20	[	[	X
ejpam-5611	343	21	a	a	PRON
ejpam-5611	343	22	,	,	PUNCT
ejpam-5611	343	23	b	b	NOUN
ejpam-5611	343	24	]	]	X
ejpam-5611	343	25	.	.	PUNCT
ejpam-5611	344	1	thus	thus	ADV
ejpam-5611	344	2	,	,	PUNCT
ejpam-5611	344	3	there	there	PRON
ejpam-5611	344	4	is	be	VERB
ejpam-5611	344	5	a	a	DET
ejpam-5611	344	6	gauge	gauge	NOUN
ejpam-5611	344	7	δ2	δ2	VERB
ejpam-5611	344	8	≤	≤	NUM
ejpam-5611	344	9	δ1	δ1	NOUN
ejpam-5611	344	10	on	on	ADP
ejpam-5611	344	11	[	[	X
ejpam-5611	344	12	a	a	DET
ejpam-5611	344	13	,	,	PUNCT
ejpam-5611	344	14	b	b	NOUN
ejpam-5611	344	15	]	]	X
ejpam-5611	344	16	such	such	ADJ
ejpam-5611	344	17	that	that	PRON
ejpam-5611	344	18	for	for	ADP
ejpam-5611	344	19	every	every	DET
ejpam-5611	344	20	δ2	δ2	VERB
ejpam-5611	344	21	-	-	PUNCT
ejpam-5611	344	22	fine	fine	NOUN
ejpam-5611	344	23	division	division	NOUN
ejpam-5611	344	24	d	d	NOUN
ejpam-5611	344	25	=	=	PRON
ejpam-5611	344	26	{	{	PUNCT
ejpam-5611	344	27	(	(	PUNCT
ejpam-5611	344	28	ξ′	ξ′	ADJ
ejpam-5611	344	29	,	,	PUNCT
ejpam-5611	344	30	ψ	ψ	PROPN
ejpam-5611	344	31	,	,	PUNCT
ejpam-5611	344	32	j	j	NOUN
ejpam-5611	344	33	)	)	PUNCT
ejpam-5611	344	34	}	}	PUNCT
ejpam-5611	344	35	of	of	ADP
ejpam-5611	344	36	[	[	X
ejpam-5611	344	37	a	a	X
ejpam-5611	344	38	,	,	PUNCT
ejpam-5611	344	39	b	b	NOUN
ejpam-5611	344	40	]	]	X
ejpam-5611	344	41	,	,	PUNCT
ejpam-5611	344	42	we	we	PRON
ejpam-5611	344	43	have∥∥∥∥∑	have∥∥∥∥∑	PUNCT
ejpam-5611	344	44	d	d	X
ejpam-5611	344	45	f(ξ′	f(ξ′	NOUN
ejpam-5611	344	46	)	)	PUNCT
ejpam-5611	344	47	·	·	PUNCT
ejpam-5611	345	1	(	(	PUNCT
ejpam-5611	345	2	1−	1−	NUM
ejpam-5611	345	3	ϕ(ξ′	ϕ(ξ′	NOUN
ejpam-5611	345	4	)	)	PUNCT
ejpam-5611	345	5	)	)	PUNCT
ejpam-5611	346	1	∫	∫	PROPN
ejpam-5611	346	2	j	j	PROPN
ejpam-5611	346	3	ψ	ψ	X
ejpam-5611	346	4	−	−	PROPN
ejpam-5611	346	5	(	(	PUNCT
ejpam-5611	346	6	p	p	NOUN
ejpam-5611	346	7	)	)	PUNCT
ejpam-5611	346	8	∫	∫	PROPN
ejpam-5611	347	1	[	[	X
ejpam-5611	347	2	a	a	X
ejpam-5611	347	3	,	,	PUNCT
ejpam-5611	347	4	b	b	NOUN
ejpam-5611	347	5	]	]	X
ejpam-5611	347	6	f	f	X
ejpam-5611	347	7	·	·	PUNCT
ejpam-5611	347	8	(	(	PUNCT
ejpam-5611	347	9	1−	1−	NUM
ejpam-5611	347	10	ϕ	ϕ	NOUN
ejpam-5611	347	11	)	)	PUNCT
ejpam-5611	347	12	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5611	347	13	g.	g.	PROPN
ejpam-5611	347	14	flores	flores	PROPN
ejpam-5611	347	15	,	,	PUNCT
ejpam-5611	347	16	a.	a.	PROPN
ejpam-5611	347	17	flores	flores	PROPN
ejpam-5611	347	18	/	/	SYM
ejpam-5611	347	19	eur	eur	PROPN
ejpam-5611	347	20	.	.	PUNCT
ejpam-5611	348	1	j.	j.	PROPN
ejpam-5611	348	2	pure	pure	PROPN
ejpam-5611	348	3	appl	appl	PROPN
ejpam-5611	348	4	.	.	PROPN
ejpam-5611	348	5	math	math	PROPN
ejpam-5611	348	6	,	,	PUNCT
ejpam-5611	348	7	18	18	NUM
ejpam-5611	348	8	(	(	PUNCT
ejpam-5611	348	9	2	2	NUM
ejpam-5611	348	10	)	)	PUNCT
ejpam-5611	348	11	(	(	PUNCT
ejpam-5611	348	12	2025	2025	NUM
ejpam-5611	348	13	)	)	PUNCT
ejpam-5611	348	14	,	,	PUNCT
ejpam-5611	348	15	5611	5611	NUM
ejpam-5611	348	16	14	14	NUM
ejpam-5611	348	17	of	of	ADP
ejpam-5611	348	18	16	16	NUM
ejpam-5611	348	19	=	=	SYM
ejpam-5611	348	20	∥∥∥∥∑	∥∥∥∥∑	PROPN
ejpam-5611	348	21	d	d	NOUN
ejpam-5611	348	22	f(ξ′	f(ξ′	NOUN
ejpam-5611	348	23	)	)	PUNCT
ejpam-5611	348	24	·	·	PUNCT
ejpam-5611	349	1	(	(	PUNCT
ejpam-5611	349	2	1−	1−	NUM
ejpam-5611	349	3	ϕ(ξ′	ϕ(ξ′	NOUN
ejpam-5611	349	4	)	)	PUNCT
ejpam-5611	349	5	)	)	PUNCT
ejpam-5611	350	1	∫	∫	PROPN
ejpam-5611	350	2	j	j	PROPN
ejpam-5611	350	3	ψ	ψ	X
ejpam-5611	350	4	−	−	PROPN
ejpam-5611	350	5	(	(	PUNCT
ejpam-5611	350	6	p	p	NOUN
ejpam-5611	350	7	)	)	PUNCT
ejpam-5611	350	8	∫	∫	PROPN
ejpam-5611	351	1	[	[	X
ejpam-5611	351	2	a	a	X
ejpam-5611	351	3	,	,	PUNCT
ejpam-5611	351	4	b	b	NOUN
ejpam-5611	351	5	]	]	X
ejpam-5611	351	6	f	f	X
ejpam-5611	352	1	+	+	CCONJ
ejpam-5611	352	2	(	(	PUNCT
ejpam-5611	352	3	p	p	X
ejpam-5611	352	4	)	)	PUNCT
ejpam-5611	352	5	∫	∫	PROPN
ejpam-5611	353	1	[	[	X
ejpam-5611	353	2	a	a	X
ejpam-5611	353	3	,	,	PUNCT
ejpam-5611	353	4	b	b	NOUN
ejpam-5611	353	5	]	]	X
ejpam-5611	353	6	f	f	X
ejpam-5611	353	7	·	·	PUNCT
ejpam-5611	353	8	(	(	PUNCT
ejpam-5611	353	9	∑	∑	PUNCT
ejpam-5611	353	10	p	p	X
ejpam-5611	353	11	φ	φ	PROPN
ejpam-5611	353	12	)	)	PUNCT
ejpam-5611	353	13	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-5611	354	1	=	=	SYM
ejpam-5611	355	1	∥∥∥∥∑	∥∥∥∥∑	PUNCT
ejpam-5611	356	1	d	d	X
ejpam-5611	356	2	f(ξ′	f(ξ′	NOUN
ejpam-5611	356	3	)	)	PUNCT
ejpam-5611	356	4	·	·	PUNCT
ejpam-5611	357	1	(	(	PUNCT
ejpam-5611	357	2	1−	1−	NUM
ejpam-5611	357	3	ϕ(ξ′	ϕ(ξ′	NOUN
ejpam-5611	357	4	)	)	PUNCT
ejpam-5611	357	5	)	)	PUNCT
ejpam-5611	358	1	∫	∫	PROPN
ejpam-5611	358	2	j	j	PROPN
ejpam-5611	358	3	ψ	ψ	X
ejpam-5611	358	4	−	−	PROPN
ejpam-5611	358	5	(	(	PUNCT
ejpam-5611	358	6	p	p	NOUN
ejpam-5611	358	7	)	)	PUNCT
ejpam-5611	358	8	∫	∫	PROPN
ejpam-5611	359	1	[	[	X
ejpam-5611	359	2	a	a	X
ejpam-5611	359	3	,	,	PUNCT
ejpam-5611	359	4	b	b	NOUN
ejpam-5611	359	5	]	]	X
ejpam-5611	359	6	f	f	PROPN
ejpam-5611	360	1	+	+	CCONJ
ejpam-5611	360	2	∑	∑	PROPN
ejpam-5611	360	3	p	p	X
ejpam-5611	360	4	∫	∫	PROPN
ejpam-5611	361	1	i	i	NOUN
ejpam-5611	361	2	f	f	PROPN
ejpam-5611	361	3	·	·	PUNCT
ejpam-5611	361	4	φ	φ	PROPN
ejpam-5611	361	5	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5611	361	6	<	<	X
ejpam-5611	361	7	ϵ	ϵ	X
ejpam-5611	361	8	3	3	NUM
ejpam-5611	361	9	,	,	PUNCT
ejpam-5611	361	10	that	that	ADV
ejpam-5611	361	11	is	is	ADV
ejpam-5611	361	12	,	,	PUNCT
ejpam-5611	361	13	∥∥∥∥∑	∥∥∥∥∑	PROPN
ejpam-5611	361	14	d	d	X
ejpam-5611	361	15	f(ξ′	f(ξ′	NOUN
ejpam-5611	361	16	)	)	PUNCT
ejpam-5611	361	17	·	·	PUNCT
ejpam-5611	362	1	(	(	PUNCT
ejpam-5611	362	2	1−	1−	NUM
ejpam-5611	362	3	ϕ(ξ′	ϕ(ξ′	NOUN
ejpam-5611	362	4	)	)	PUNCT
ejpam-5611	362	5	)	)	PUNCT
ejpam-5611	363	1	∫	∫	PROPN
ejpam-5611	364	1	j	j	PROPN
ejpam-5611	364	2	ψ	ψ	PROPN
ejpam-5611	365	1	+	+	CCONJ
ejpam-5611	365	2	∑	∑	PROPN
ejpam-5611	365	3	p	p	X
ejpam-5611	365	4	∫	∫	PROPN
ejpam-5611	366	1	i	i	NOUN
ejpam-5611	366	2	f	f	PROPN
ejpam-5611	366	3	·	·	PUNCT
ejpam-5611	366	4	φ−	φ−	PROPN
ejpam-5611	366	5	(	(	PUNCT
ejpam-5611	366	6	p	p	NOUN
ejpam-5611	366	7	)	)	PUNCT
ejpam-5611	366	8	∫	∫	PROPN
ejpam-5611	367	1	[	[	X
ejpam-5611	367	2	a	a	X
ejpam-5611	367	3	,	,	PUNCT
ejpam-5611	367	4	b	b	NOUN
ejpam-5611	367	5	]	]	X
ejpam-5611	367	6	f	f	X
ejpam-5611	367	7	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5611	367	8	<	<	X
ejpam-5611	367	9	ϵ	ϵ	X
ejpam-5611	367	10	3	3	NUM
ejpam-5611	367	11	.	.	PUNCT
ejpam-5611	368	1	(	(	PUNCT
ejpam-5611	368	2	3.20	3.20	NUM
ejpam-5611	368	3	)	)	PUNCT
ejpam-5611	368	4	now	now	ADV
ejpam-5611	368	5	,	,	PUNCT
ejpam-5611	368	6	since	since	SCONJ
ejpam-5611	368	7	p	p	NOUN
ejpam-5611	368	8	∪	∪	X
ejpam-5611	368	9	{	{	PUNCT
ejpam-5611	368	10	(	(	PUNCT
ejpam-5611	368	11	ξ	ξ	PROPN
ejpam-5611	368	12	,	,	PUNCT
ejpam-5611	368	13	j	j	PROPN
ejpam-5611	368	14	,	,	PUNCT
ejpam-5611	368	15	(	(	PUNCT
ejpam-5611	368	16	1	1	NUM
ejpam-5611	368	17	−	−	NOUN
ejpam-5611	368	18	ϕ)ψ	ϕ)ψ	NOUN
ejpam-5611	368	19	)	)	PUNCT
ejpam-5611	368	20	:	:	PUNCT
ejpam-5611	368	21	(	(	PUNCT
ejpam-5611	368	22	ξ	ξ	X
ejpam-5611	368	23	,	,	PUNCT
ejpam-5611	368	24	j	j	PROPN
ejpam-5611	368	25	,	,	PUNCT
ejpam-5611	368	26	ψ	ψ	X
ejpam-5611	368	27	)	)	PUNCT
ejpam-5611	368	28	∈	∈	PROPN
ejpam-5611	368	29	d	d	X
ejpam-5611	368	30	}	}	PUNCT
ejpam-5611	368	31	is	be	AUX
ejpam-5611	368	32	also	also	ADV
ejpam-5611	368	33	a	a	DET
ejpam-5611	368	34	δ	δ	NOUN
ejpam-5611	368	35	-	-	PUNCT
ejpam-5611	368	36	fine	fine	ADJ
ejpam-5611	368	37	division	division	NOUN
ejpam-5611	368	38	of	of	ADP
ejpam-5611	368	39	[	[	X
ejpam-5611	368	40	a	a	X
ejpam-5611	368	41	,	,	PUNCT
ejpam-5611	368	42	b	b	NOUN
ejpam-5611	368	43	]	]	PUNCT
ejpam-5611	368	44	and	and	CCONJ
ejpam-5611	368	45	by	by	ADP
ejpam-5611	368	46	integrability	integrability	NOUN
ejpam-5611	368	47	of	of	ADP
ejpam-5611	368	48	f	f	PROPN
ejpam-5611	368	49	,	,	PUNCT
ejpam-5611	368	50	we	we	PRON
ejpam-5611	368	51	have∥∥∥∥∑	have∥∥∥∥∑	VERB
ejpam-5611	368	52	p	p	NOUN
ejpam-5611	368	53	f(ξ	f(ξ	NOUN
ejpam-5611	368	54	)	)	PUNCT
ejpam-5611	368	55	∫	∫	NOUN
ejpam-5611	369	1	i	i	PRON
ejpam-5611	369	2	φ+	φ+	VERB
ejpam-5611	369	3	∑	∑	PROPN
ejpam-5611	369	4	d	d	PROPN
ejpam-5611	369	5	f(ξ′	f(ξ′	PROPN
ejpam-5611	369	6	)	)	PUNCT
ejpam-5611	369	7	∫	∫	PROPN
ejpam-5611	369	8	j	j	PROPN
ejpam-5611	370	1	(	(	PUNCT
ejpam-5611	370	2	1−	1−	NUM
ejpam-5611	370	3	ϕ)ψ	ϕ)ψ	NOUN
ejpam-5611	371	1	−	−	PROPN
ejpam-5611	371	2	(	(	PUNCT
ejpam-5611	371	3	p	p	NOUN
ejpam-5611	371	4	)	)	PUNCT
ejpam-5611	371	5	∫	∫	PROPN
ejpam-5611	372	1	[	[	X
ejpam-5611	372	2	a	a	X
ejpam-5611	372	3	,	,	PUNCT
ejpam-5611	372	4	b	b	NOUN
ejpam-5611	372	5	]	]	X
ejpam-5611	372	6	f	f	X
ejpam-5611	372	7	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5611	372	8	<	<	X
ejpam-5611	372	9	ϵ	ϵ	X
ejpam-5611	372	10	3	3	NUM
ejpam-5611	372	11	.	.	PUNCT
ejpam-5611	373	1	(	(	PUNCT
ejpam-5611	373	2	3.21	3.21	NUM
ejpam-5611	373	3	)	)	PUNCT
ejpam-5611	373	4	observe	observe	VERB
ejpam-5611	373	5	that	that	SCONJ
ejpam-5611	373	6	by	by	ADP
ejpam-5611	373	7	(	(	PUNCT
ejpam-5611	373	8	3.19),∥∥∥∥∑	3.19),∥∥∥∥∑	NUM
ejpam-5611	373	9	d	d	NUM
ejpam-5611	373	10	f(ξ′)(1−	f(ξ′)(1−	ADJ
ejpam-5611	373	11	ϕ(ξ′	ϕ(ξ′	NOUN
ejpam-5611	373	12	)	)	PUNCT
ejpam-5611	373	13	)	)	PUNCT
ejpam-5611	374	1	∫	∫	PROPN
ejpam-5611	374	2	j	j	PROPN
ejpam-5611	374	3	ψ	ψ	PROPN
ejpam-5611	374	4	−	−	PROPN
ejpam-5611	374	5	∑	∑	PROPN
ejpam-5611	374	6	d	d	PROPN
ejpam-5611	374	7	f(ξ′	f(ξ′	PROPN
ejpam-5611	374	8	)	)	PUNCT
ejpam-5611	374	9	∫	∫	PROPN
ejpam-5611	375	1	j	j	PROPN
ejpam-5611	375	2	(	(	PUNCT
ejpam-5611	375	3	1−	1−	NUM
ejpam-5611	375	4	ϕ)ψ	ϕ)ψ	NOUN
ejpam-5611	375	5	∥∥∥∥	∥∥∥∥	NUM
ejpam-5611	375	6	=	=	SYM
ejpam-5611	375	7	∥∥∥∥∑	∥∥∥∥∑	PUNCT
ejpam-5611	376	1	d	d	X
ejpam-5611	376	2	{	{	PUNCT
ejpam-5611	376	3	f(ξ′	f(ξ′	NOUN
ejpam-5611	376	4	)	)	PUNCT
ejpam-5611	376	5	·	·	PUNCT
ejpam-5611	377	1	∫	∫	PROPN
ejpam-5611	377	2	j	j	PROPN
ejpam-5611	377	3	[	[	PUNCT
ejpam-5611	377	4	ϕ−	ϕ−	PROPN
ejpam-5611	377	5	ϕ(ξ′	ϕ(ξ′	NOUN
ejpam-5611	377	6	)	)	PUNCT
ejpam-5611	377	7	]	]	PUNCT
ejpam-5611	378	1	ψ	ψ	X
ejpam-5611	378	2	}	}	PUNCT
ejpam-5611	378	3	∥∥∥∥	∥∥∥∥	NUM
ejpam-5611	378	4	≤	≤	NUM
ejpam-5611	378	5	∥∥∥∥∑	∥∥∥∥∑	PROPN
ejpam-5611	379	1	d	d	NOUN
ejpam-5611	379	2	{	{	PUNCT
ejpam-5611	379	3	f(ξ′	f(ξ′	NOUN
ejpam-5611	379	4	)	)	PUNCT
ejpam-5611	379	5	·	·	PUNCT
ejpam-5611	380	1	∫	∫	PROPN
ejpam-5611	380	2	j	j	PROPN
ejpam-5611	380	3	sup	sup	PROPN
ejpam-5611	380	4	{	{	PUNCT
ejpam-5611	380	5	|ϕ(x)−	|ϕ(x)−	PROPN
ejpam-5611	380	6	ϕ(ξ′)|	ϕ(ξ′)|	PROPN
ejpam-5611	380	7	:	:	PUNCT
ejpam-5611	380	8	x	x	SYM
ejpam-5611	380	9	∈	∈	PROPN
ejpam-5611	380	10	b(ξ′	b(ξ′	NOUN
ejpam-5611	380	11	,	,	PUNCT
ejpam-5611	380	12	δ1(ξ	δ1(ξ	PROPN
ejpam-5611	380	13	′	′	NUM
ejpam-5611	380	14	)	)	PUNCT
ejpam-5611	380	15	)	)	PUNCT
ejpam-5611	380	16	}	}	PUNCT
ejpam-5611	380	17	·	·	PUNCT
ejpam-5611	381	1	ψ	ψ	X
ejpam-5611	381	2	}	}	PUNCT
ejpam-5611	381	3	∥∥∥∥	∥∥∥∥	NUM
ejpam-5611	381	4	=	=	SYM
ejpam-5611	381	5	∥∥∥∥∑	∥∥∥∥∑	PUNCT
ejpam-5611	381	6	d	d	X
ejpam-5611	381	7	{	{	PUNCT
ejpam-5611	381	8	f(ξ′	f(ξ′	NOUN
ejpam-5611	381	9	)	)	PUNCT
ejpam-5611	381	10	·	·	PUNCT
ejpam-5611	382	1	sup	sup	INTJ
ejpam-5611	382	2	{	{	PUNCT
ejpam-5611	382	3	|ϕ(x)−	|ϕ(x)−	NOUN
ejpam-5611	382	4	ϕ(ξ′)|	ϕ(ξ′)|	PROPN
ejpam-5611	382	5	:	:	PUNCT
ejpam-5611	382	6	x	x	SYM
ejpam-5611	382	7	∈	∈	PROPN
ejpam-5611	382	8	b(ξ′	b(ξ′	NOUN
ejpam-5611	382	9	,	,	PUNCT
ejpam-5611	382	10	δ1(ξ	δ1(ξ	PROPN
ejpam-5611	382	11	′	′	NUM
ejpam-5611	382	12	)	)	PUNCT
ejpam-5611	382	13	)	)	PUNCT
ejpam-5611	382	14	}	}	PUNCT
ejpam-5611	382	15	·	·	PUNCT
ejpam-5611	383	1	∫	∫	PROPN
ejpam-5611	383	2	j	j	PROPN
ejpam-5611	383	3	ψ	ψ	PROPN
ejpam-5611	383	4	}	}	PUNCT
ejpam-5611	383	5	∥∥∥∥	∥∥∥∥	NUM
ejpam-5611	383	6	≤	≤	NUM
ejpam-5611	383	7	∑	∑	PUNCT
ejpam-5611	383	8	d	d	PROPN
ejpam-5611	383	9	{	{	PUNCT
ejpam-5611	383	10	∥∥f(ξ′)∥∥	∥∥f(ξ′)∥∥	PROPN
ejpam-5611	383	11	·	·	PUNCT
ejpam-5611	383	12	sup	sup	X
ejpam-5611	383	13	{	{	PUNCT
ejpam-5611	383	14	|ϕ(x)−	|ϕ(x)−	NOUN
ejpam-5611	383	15	ϕ(ξ′)|	ϕ(ξ′)|	PROPN
ejpam-5611	383	16	:	:	PUNCT
ejpam-5611	383	17	x	x	SYM
ejpam-5611	383	18	∈	∈	PROPN
ejpam-5611	383	19	b(ξ′	b(ξ′	NOUN
ejpam-5611	383	20	,	,	PUNCT
ejpam-5611	383	21	δ1(ξ	δ1(ξ	PROPN
ejpam-5611	383	22	′	′	NUM
ejpam-5611	383	23	)	)	PUNCT
ejpam-5611	383	24	)	)	PUNCT
ejpam-5611	383	25	}	}	PUNCT
ejpam-5611	383	26	·	·	PUNCT
ejpam-5611	384	1	∫	∫	PROPN
ejpam-5611	384	2	j	j	PROPN
ejpam-5611	384	3	ψ	ψ	PROPN
ejpam-5611	384	4	}	}	PUNCT
ejpam-5611	384	5	<	<	X
ejpam-5611	384	6	ϵ	ϵ	X
ejpam-5611	384	7	3	3	NUM
ejpam-5611	384	8	;	;	PUNCT
ejpam-5611	384	9	that	that	PRON
ejpam-5611	384	10	is	be	AUX
ejpam-5611	384	11	,	,	PUNCT
ejpam-5611	384	12	∥∥∥∥∑	∥∥∥∥∑	PROPN
ejpam-5611	385	1	d	d	X
ejpam-5611	385	2	f(ξ′)(1−	f(ξ′)(1−	PROPN
ejpam-5611	385	3	ϕ(ξ′	ϕ(ξ′	NOUN
ejpam-5611	385	4	)	)	PUNCT
ejpam-5611	385	5	)	)	PUNCT
ejpam-5611	386	1	∫	∫	PROPN
ejpam-5611	386	2	j	j	PROPN
ejpam-5611	386	3	ψ	ψ	PROPN
ejpam-5611	386	4	−	−	PROPN
ejpam-5611	386	5	∑	∑	PROPN
ejpam-5611	386	6	d	d	PROPN
ejpam-5611	386	7	f(ξ′	f(ξ′	PROPN
ejpam-5611	386	8	)	)	PUNCT
ejpam-5611	386	9	∫	∫	PROPN
ejpam-5611	387	1	j	j	PROPN
ejpam-5611	387	2	(	(	PUNCT
ejpam-5611	387	3	1−	1−	NUM
ejpam-5611	387	4	ϕ)ψ	ϕ)ψ	NOUN
ejpam-5611	387	5	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-5611	387	6	<	<	X
ejpam-5611	387	7	ϵ	ϵ	X
ejpam-5611	387	8	3	3	NUM
ejpam-5611	387	9	.	.	PUNCT
ejpam-5611	388	1	(	(	PUNCT
ejpam-5611	388	2	3.22	3.22	NUM
ejpam-5611	388	3	)	)	PUNCT
ejpam-5611	388	4	therefore	therefore	ADV
ejpam-5611	388	5	,	,	PUNCT
ejpam-5611	388	6	by	by	ADP
ejpam-5611	388	7	(	(	PUNCT
ejpam-5611	388	8	3.20	3.20	NUM
ejpam-5611	388	9	)	)	PUNCT
ejpam-5611	388	10	,	,	PUNCT
ejpam-5611	388	11	(	(	PUNCT
ejpam-5611	388	12	3.21	3.21	NUM
ejpam-5611	388	13	)	)	PUNCT
ejpam-5611	388	14	,	,	PUNCT
ejpam-5611	388	15	and	and	CCONJ
ejpam-5611	388	16	(	(	PUNCT
ejpam-5611	388	17	3.22)∥∥∥∥∑	3.22)∥∥∥∥∑	NUM
ejpam-5611	388	18	p	p	X
ejpam-5611	388	19	(	(	PUNCT
ejpam-5611	388	20	f(ξ	f(ξ	PROPN
ejpam-5611	388	21	)	)	PUNCT
ejpam-5611	388	22	∫	∫	NOUN
ejpam-5611	389	1	i	i	PRON
ejpam-5611	389	2	φ−	φ−	PROPN
ejpam-5611	390	1	∫	∫	INTJ
ejpam-5611	391	1	i	i	PRON
ejpam-5611	391	2	fφ	fφ	VERB
ejpam-5611	391	3	)	)	PUNCT
ejpam-5611	391	4	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-5611	391	5	=	=	SYM
ejpam-5611	391	6	∥∥∥∥∑	∥∥∥∥∑	PROPN
ejpam-5611	392	1	p	p	NOUN
ejpam-5611	392	2	f(ξ	f(ξ	PROPN
ejpam-5611	392	3	)	)	PUNCT
ejpam-5611	392	4	∫	∫	PROPN
ejpam-5611	393	1	i	i	PRON
ejpam-5611	393	2	φ	φ	NUM
ejpam-5611	393	3	−	−	PROPN
ejpam-5611	393	4	(	(	PUNCT
ejpam-5611	393	5	p	p	NOUN
ejpam-5611	393	6	)	)	PUNCT
ejpam-5611	393	7	∫	∫	PROPN
ejpam-5611	394	1	[	[	X
ejpam-5611	394	2	a	a	X
ejpam-5611	394	3	,	,	PUNCT
ejpam-5611	394	4	b	b	NOUN
ejpam-5611	394	5	]	]	X
ejpam-5611	394	6	f	f	X
ejpam-5611	395	1	+	+	CCONJ
ejpam-5611	395	2	(	(	PUNCT
ejpam-5611	395	3	p	p	X
ejpam-5611	395	4	)	)	PUNCT
ejpam-5611	395	5	∫	∫	PROPN
ejpam-5611	396	1	[	[	X
ejpam-5611	396	2	a	a	X
ejpam-5611	396	3	,	,	PUNCT
ejpam-5611	396	4	b	b	X
ejpam-5611	396	5	]	]	X
ejpam-5611	396	6	f	f	X
ejpam-5611	396	7	−	−	NOUN
ejpam-5611	396	8	∑	∑	PUNCT
ejpam-5611	396	9	d	d	X
ejpam-5611	396	10	f(ξ′)(1−	f(ξ′)(1−	ADJ
ejpam-5611	396	11	ϕ(ξ′	ϕ(ξ′	NOUN
ejpam-5611	396	12	)	)	PUNCT
ejpam-5611	396	13	)	)	PUNCT
ejpam-5611	397	1	∫	∫	PROPN
ejpam-5611	397	2	j	j	PROPN
ejpam-5611	397	3	ψ	ψ	PROPN
ejpam-5611	397	4	+	+	CCONJ
ejpam-5611	397	5	∑	∑	PROPN
ejpam-5611	397	6	d	d	PRON
ejpam-5611	397	7	f(ξ′)(1−	f(ξ′)(1−	ADJ
ejpam-5611	397	8	ϕ(ξ′	ϕ(ξ′	NOUN
ejpam-5611	397	9	)	)	PUNCT
ejpam-5611	397	10	)	)	PUNCT
ejpam-5611	398	1	∫	∫	PROPN
ejpam-5611	398	2	j	j	PROPN
ejpam-5611	398	3	ψ	ψ	PROPN
ejpam-5611	398	4	−	−	PROPN
ejpam-5611	398	5	∑	∑	PROPN
ejpam-5611	398	6	d	d	PROPN
ejpam-5611	398	7	f(ξ′	f(ξ′	PROPN
ejpam-5611	398	8	)	)	PUNCT
ejpam-5611	398	9	∫	∫	PROPN
ejpam-5611	399	1	j	j	PROPN
ejpam-5611	399	2	(	(	PUNCT
ejpam-5611	399	3	1−	1−	NUM
ejpam-5611	399	4	ϕ)ψ	ϕ)ψ	PROPN
ejpam-5611	399	5	g.	g.	PROPN
ejpam-5611	399	6	flores	flores	PROPN
ejpam-5611	399	7	,	,	PUNCT
ejpam-5611	399	8	a.	a.	PROPN
ejpam-5611	399	9	flores	flores	PROPN
ejpam-5611	399	10	/	/	SYM
ejpam-5611	399	11	eur	eur	PROPN
ejpam-5611	399	12	.	.	PUNCT
ejpam-5611	400	1	j.	j.	PROPN
ejpam-5611	400	2	pure	pure	PROPN
ejpam-5611	400	3	appl	appl	PROPN
ejpam-5611	400	4	.	.	PROPN
ejpam-5611	400	5	math	math	PROPN
ejpam-5611	400	6	,	,	PUNCT
ejpam-5611	400	7	18	18	NUM
ejpam-5611	400	8	(	(	PUNCT
ejpam-5611	400	9	2	2	NUM
ejpam-5611	400	10	)	)	PUNCT
ejpam-5611	400	11	(	(	PUNCT
ejpam-5611	400	12	2025	2025	NUM
ejpam-5611	400	13	)	)	PUNCT
ejpam-5611	400	14	,	,	PUNCT
ejpam-5611	400	15	5611	5611	NUM
ejpam-5611	400	16	15	15	NUM
ejpam-5611	400	17	of	of	ADP
ejpam-5611	400	18	16	16	NUM
ejpam-5611	400	19	+	+	CCONJ
ejpam-5611	400	20	∑	∑	PROPN
ejpam-5611	400	21	d	d	PROPN
ejpam-5611	400	22	f(ξ′	f(ξ′	NOUN
ejpam-5611	400	23	)	)	PUNCT
ejpam-5611	400	24	∫	∫	PROPN
ejpam-5611	400	25	j	j	PROPN
ejpam-5611	400	26	(	(	PUNCT
ejpam-5611	400	27	1−	1−	NUM
ejpam-5611	400	28	ϕ)ψ	ϕ)ψ	NOUN
ejpam-5611	401	1	−	−	ADP
ejpam-5611	401	2	∑	∑	PUNCT
ejpam-5611	402	1	p	p	X
ejpam-5611	402	2	∫	∫	PROPN
ejpam-5611	403	1	i	i	PRON
ejpam-5611	403	2	fφ	fφ	VERB
ejpam-5611	403	3	∥∥∥∥	∥∥∥∥	NOUN
ejpam-5611	403	4	≤	≤	NUM
ejpam-5611	404	1	∥∥∥∥∑	∥∥∥∥∑	PROPN
ejpam-5611	405	1	p	p	ADJ
ejpam-5611	405	2	f(ξ	f(ξ	PROPN
ejpam-5611	405	3	)	)	PUNCT
ejpam-5611	405	4	∫	∫	NOUN
ejpam-5611	406	1	i	i	PRON
ejpam-5611	406	2	φ+	φ+	VERB
ejpam-5611	406	3	∑	∑	PROPN
ejpam-5611	406	4	d	d	PROPN
ejpam-5611	406	5	f(ξ′	f(ξ′	PROPN
ejpam-5611	406	6	)	)	PUNCT
ejpam-5611	406	7	∫	∫	PROPN
ejpam-5611	406	8	j	j	PROPN
ejpam-5611	407	1	(	(	PUNCT
ejpam-5611	407	2	1−	1−	NUM
ejpam-5611	407	3	ϕ)ψ	ϕ)ψ	NOUN
ejpam-5611	408	1	−	−	PROPN
ejpam-5611	408	2	(	(	PUNCT
ejpam-5611	408	3	p	p	NOUN
ejpam-5611	408	4	)	)	PUNCT
ejpam-5611	408	5	∫	∫	PROPN
ejpam-5611	409	1	[	[	X
ejpam-5611	409	2	a	a	X
ejpam-5611	409	3	,	,	PUNCT
ejpam-5611	409	4	b	b	NOUN
ejpam-5611	409	5	]	]	X
ejpam-5611	409	6	f	f	X
ejpam-5611	409	7	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5611	410	1	+	+	CCONJ
ejpam-5611	410	2	∥∥∥∥(p	∥∥∥∥(p	NOUN
ejpam-5611	410	3	)	)	PUNCT
ejpam-5611	410	4	∫	∫	PROPN
ejpam-5611	411	1	[	[	X
ejpam-5611	411	2	a	a	X
ejpam-5611	411	3	,	,	PUNCT
ejpam-5611	411	4	b	b	X
ejpam-5611	411	5	]	]	X
ejpam-5611	411	6	f	f	PROPN
ejpam-5611	411	7	−	−	NOUN
ejpam-5611	412	1	∑	∑	PUNCT
ejpam-5611	413	1	p	p	X
ejpam-5611	413	2	∫	∫	PROPN
ejpam-5611	414	1	i	i	PRON
ejpam-5611	414	2	fφ−	fφ−	PUNCT
ejpam-5611	414	3	∑	∑	PUNCT
ejpam-5611	414	4	d	d	X
ejpam-5611	414	5	f(ξ′)(1−	f(ξ′)(1−	ADJ
ejpam-5611	414	6	ϕ(ξ′	ϕ(ξ′	NOUN
ejpam-5611	414	7	)	)	PUNCT
ejpam-5611	414	8	)	)	PUNCT
ejpam-5611	415	1	∫	∫	PROPN
ejpam-5611	416	1	i	i	PRON
ejpam-5611	416	2	ψ	ψ	PROPN
ejpam-5611	416	3	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-5611	417	1	+	+	CCONJ
ejpam-5611	417	2	∥∥∥∥∑	∥∥∥∥∑	PROPN
ejpam-5611	417	3	d	d	X
ejpam-5611	417	4	f(ξ′)(1−	f(ξ′)(1−	PROPN
ejpam-5611	417	5	ϕ(ξ′	ϕ(ξ′	NOUN
ejpam-5611	417	6	)	)	PUNCT
ejpam-5611	417	7	)	)	PUNCT
ejpam-5611	418	1	∫	∫	PROPN
ejpam-5611	418	2	j	j	PROPN
ejpam-5611	418	3	ψ	ψ	PROPN
ejpam-5611	418	4	−	−	PROPN
ejpam-5611	418	5	∑	∑	PROPN
ejpam-5611	418	6	d	d	PROPN
ejpam-5611	418	7	f(ξ′	f(ξ′	PROPN
ejpam-5611	418	8	)	)	PUNCT
ejpam-5611	418	9	∫	∫	PROPN
ejpam-5611	419	1	j	j	PROPN
ejpam-5611	419	2	(	(	PUNCT
ejpam-5611	419	3	1−	1−	NUM
ejpam-5611	419	4	ϕ)ψ	ϕ)ψ	NOUN
ejpam-5611	419	5	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-5611	419	6	<	<	X
ejpam-5611	419	7	ϵ	ϵ	X
ejpam-5611	419	8	3	3	NUM
ejpam-5611	419	9	+	+	CCONJ
ejpam-5611	419	10	ϵ	ϵ	SYM
ejpam-5611	419	11	3	3	NUM
ejpam-5611	419	12	+	+	CCONJ
ejpam-5611	419	13	ϵ	ϵ	SYM
ejpam-5611	419	14	3	3	NUM
ejpam-5611	419	15	=	=	SYM
ejpam-5611	419	16	ϵ.	ϵ.	NOUN
ejpam-5611	419	17	and	and	CCONJ
ejpam-5611	419	18	the	the	DET
ejpam-5611	419	19	result	result	NOUN
ejpam-5611	419	20	follows	follow	VERB
ejpam-5611	419	21	.	.	PUNCT
ejpam-5611	420	1	□	□	PUNCT
ejpam-5611	420	2	corollary	corollary	ADJ
ejpam-5611	420	3	1	1	NUM
ejpam-5611	420	4	.	.	PUNCT
ejpam-5611	421	1	in	in	ADP
ejpam-5611	421	2	view	view	NOUN
ejpam-5611	421	3	of	of	ADP
ejpam-5611	421	4	the	the	DET
ejpam-5611	421	5	conditions	condition	NOUN
ejpam-5611	421	6	of	of	ADP
ejpam-5611	421	7	theorem	theorem	NOUN
ejpam-5611	421	8	2	2	NUM
ejpam-5611	421	9	,	,	PUNCT
ejpam-5611	421	10	if	if	SCONJ
ejpam-5611	421	11	in	in	ADP
ejpam-5611	421	12	addition	addition	NOUN
ejpam-5611	421	13	that	that	SCONJ
ejpam-5611	421	14	x	x	PRON
ejpam-5611	421	15	is	be	AUX
ejpam-5611	421	16	a	a	DET
ejpam-5611	421	17	finite	finite	ADJ
ejpam-5611	421	18	dimensional	dimensional	ADJ
ejpam-5611	421	19	banach	banach	NOUN
ejpam-5611	421	20	space	space	NOUN
ejpam-5611	421	21	,	,	PUNCT
ejpam-5611	421	22	then	then	ADV
ejpam-5611	421	23	for	for	ADP
ejpam-5611	421	24	every	every	DET
ejpam-5611	421	25	ϵ	ϵ	PROPN
ejpam-5611	421	26	>	>	X
ejpam-5611	421	27	0	0	NUM
ejpam-5611	421	28	,	,	PUNCT
ejpam-5611	421	29	there	there	PRON
ejpam-5611	421	30	exists	exist	VERB
ejpam-5611	421	31	a	a	DET
ejpam-5611	421	32	gauge	gauge	NOUN
ejpam-5611	421	33	δ	δ	NOUN
ejpam-5611	421	34	on	on	ADP
ejpam-5611	421	35	[	[	X
ejpam-5611	421	36	a	a	DET
ejpam-5611	421	37	,	,	PUNCT
ejpam-5611	421	38	b	b	NOUN
ejpam-5611	421	39	]	]	X
ejpam-5611	421	40	such	such	ADJ
ejpam-5611	421	41	that	that	PRON
ejpam-5611	421	42	for	for	ADP
ejpam-5611	421	43	any	any	DET
ejpam-5611	421	44	δ	δ	NOUN
ejpam-5611	421	45	-	-	PUNCT
ejpam-5611	421	46	fine	fine	ADJ
ejpam-5611	421	47	partial	partial	ADJ
ejpam-5611	421	48	division	division	NOUN
ejpam-5611	421	49	p	p	NOUN
ejpam-5611	421	50	=	=	PUNCT
ejpam-5611	421	51	{	{	PUNCT
ejpam-5611	421	52	(	(	PUNCT
ejpam-5611	421	53	ξ	ξ	PROPN
ejpam-5611	421	54	,	,	PUNCT
ejpam-5611	421	55	φ	φ	PROPN
ejpam-5611	421	56	,	,	PUNCT
ejpam-5611	421	57	i	i	NOUN
ejpam-5611	421	58	)	)	PUNCT
ejpam-5611	421	59	}	}	PUNCT
ejpam-5611	421	60	of	of	ADP
ejpam-5611	421	61	[	[	X
ejpam-5611	421	62	a	a	X
ejpam-5611	421	63	,	,	PUNCT
ejpam-5611	421	64	b	b	NOUN
ejpam-5611	421	65	]	]	X
ejpam-5611	421	66	,	,	PUNCT
ejpam-5611	421	67	we	we	PRON
ejpam-5611	421	68	have∑	have∑	VERB
ejpam-5611	421	69	p	p	NOUN
ejpam-5611	421	70	∥∥∥∥f(ξ)∫	∥∥∥∥f(ξ)∫	VERB
ejpam-5611	421	71	i	i	PRON
ejpam-5611	421	72	φ−	φ−	PROPN
ejpam-5611	421	73	(	(	PUNCT
ejpam-5611	421	74	p	p	NOUN
ejpam-5611	421	75	)	)	PUNCT
ejpam-5611	421	76	∫	∫	NOUN
ejpam-5611	422	1	i	i	PRON
ejpam-5611	422	2	fφ	fφ	VERB
ejpam-5611	422	3	∥∥∥∥	∥∥∥∥	NOUN
ejpam-5611	422	4	<	<	X
ejpam-5611	422	5	ϵ.	ϵ.	NOUN
ejpam-5611	422	6	proof	proof	NOUN
ejpam-5611	422	7	:	:	PUNCT
ejpam-5611	422	8	note	note	VERB
ejpam-5611	422	9	that	that	SCONJ
ejpam-5611	422	10	each	each	DET
ejpam-5611	422	11	norms	norm	NOUN
ejpam-5611	422	12	defined	define	VERB
ejpam-5611	422	13	on	on	ADP
ejpam-5611	422	14	finite	finite	ADJ
ejpam-5611	422	15	dimensional	dimensional	ADJ
ejpam-5611	422	16	normed	normed	ADJ
ejpam-5611	422	17	spaces	space	NOUN
ejpam-5611	422	18	are	be	AUX
ejpam-5611	422	19	equivalent	equivalent	ADJ
ejpam-5611	422	20	.	.	PUNCT
ejpam-5611	423	1	the	the	DET
ejpam-5611	423	2	proof	proof	NOUN
ejpam-5611	423	3	is	be	AUX
ejpam-5611	423	4	complete	complete	ADJ
ejpam-5611	423	5	by	by	ADP
ejpam-5611	423	6	considering	consider	VERB
ejpam-5611	423	7	each	each	DET
ejpam-5611	423	8	components	component	NOUN
ejpam-5611	423	9	of	of	ADP
ejpam-5611	423	10	x	x	PRON
ejpam-5611	423	11	,	,	PUNCT
ejpam-5611	423	12	endowed	endow	VERB
ejpam-5611	423	13	with	with	ADP
ejpam-5611	423	14	,	,	PUNCT
ejpam-5611	423	15	perhaps	perhaps	ADV
ejpam-5611	423	16	,	,	PUNCT
ejpam-5611	423	17	the	the	DET
ejpam-5611	423	18	maximum	maximum	ADJ
ejpam-5611	423	19	norm	norm	NOUN
ejpam-5611	423	20	.	.	PUNCT
ejpam-5611	424	1	□	□	PUNCT
ejpam-5611	424	2	acknowledgements	acknowledgement	NOUN
ejpam-5611	424	3	this	this	DET
ejpam-5611	424	4	paper	paper	NOUN
ejpam-5611	424	5	is	be	AUX
ejpam-5611	424	6	dedicated	dedicate	VERB
ejpam-5611	424	7	to	to	ADP
ejpam-5611	424	8	the	the	DET
ejpam-5611	424	9	memory	memory	NOUN
ejpam-5611	424	10	of	of	ADP
ejpam-5611	424	11	our	our	PRON
ejpam-5611	424	12	mentor	mentor	NOUN
ejpam-5611	424	13	dr	dr	PROPN
ejpam-5611	424	14	.	.	PROPN
ejpam-5611	424	15	julius	julius	PROPN
ejpam-5611	424	16	v.	v.	PROPN
ejpam-5611	424	17	benitez	benitez	PROPN
ejpam-5611	424	18	.	.	PUNCT
ejpam-5611	425	1	the	the	DET
ejpam-5611	425	2	authors	author	NOUN
ejpam-5611	425	3	would	would	AUX
ejpam-5611	425	4	like	like	VERB
ejpam-5611	425	5	to	to	PART
ejpam-5611	425	6	thank	thank	VERB
ejpam-5611	425	7	the	the	DET
ejpam-5611	425	8	central	central	PROPN
ejpam-5611	425	9	mindanao	mindanao	PROPN
ejpam-5611	425	10	university	university	PROPN
ejpam-5611	425	11	through	through	ADP
ejpam-5611	425	12	its	its	PRON
ejpam-5611	425	13	research	research	NOUN
ejpam-5611	425	14	office	office	NOUN
ejpam-5611	425	15	for	for	ADP
ejpam-5611	425	16	the	the	DET
ejpam-5611	425	17	support	support	NOUN
ejpam-5611	425	18	of	of	ADP
ejpam-5611	425	19	this	this	DET
ejpam-5611	425	20	paper	paper	NOUN
ejpam-5611	425	21	.	.	PUNCT
ejpam-5611	426	1	references	reference	NOUN
ejpam-5611	426	2	[	[	X
ejpam-5611	426	3	1	1	X
ejpam-5611	426	4	]	]	PUNCT
ejpam-5611	426	5	j.	j.	PROPN
ejpam-5611	426	6	jarnik	jarnik	PROPN
ejpam-5611	426	7	and	and	CCONJ
ejpam-5611	426	8	j.	j.	PROPN
ejpam-5611	426	9	kurzweil	kurzweil	PROPN
ejpam-5611	426	10	.	.	PUNCT
ejpam-5611	427	1	a	a	DET
ejpam-5611	427	2	nonabsolutely	nonabsolutely	ADV
ejpam-5611	427	3	convergent	convergent	ADJ
ejpam-5611	427	4	integral	integral	ADJ
ejpam-5611	427	5	which	which	PRON
ejpam-5611	427	6	admits	admit	VERB
ejpam-5611	427	7	transformation	transformation	NOUN
ejpam-5611	427	8	and	and	CCONJ
ejpam-5611	427	9	can	can	AUX
ejpam-5611	427	10	be	be	AUX
ejpam-5611	427	11	used	use	VERB
ejpam-5611	427	12	for	for	ADP
ejpam-5611	427	13	integration	integration	NOUN
ejpam-5611	427	14	on	on	ADP
ejpam-5611	427	15	manifolds	manifold	NOUN
ejpam-5611	427	16	.	.	PUNCT
ejpam-5611	428	1	czechoslovak	czechoslovak	ADJ
ejpam-5611	428	2	math	math	NOUN
ejpam-5611	428	3	.	.	PUNCT
ejpam-5611	429	1	j.	j.	PROPN
ejpam-5611	429	2	,	,	PUNCT
ejpam-5611	429	3	35(1):116	35(1):116	PROPN
ejpam-5611	429	4	–	–	PUNCT
ejpam-5611	429	5	139	139	NUM
ejpam-5611	429	6	,	,	PUNCT
ejpam-5611	429	7	1985	1985	NUM
ejpam-5611	429	8	.	.	PUNCT
ejpam-5611	430	1	[	[	X
ejpam-5611	430	2	2	2	X
ejpam-5611	430	3	]	]	PUNCT
ejpam-5611	430	4	v.	v.	ADP
ejpam-5611	430	5	boonpogkrong	boonpogkrong	PROPN
ejpam-5611	430	6	.	.	PUNCT
ejpam-5611	431	1	kursweil	kursweil	NOUN
ejpam-5611	431	2	-	-	PUNCT
ejpam-5611	431	3	henstock	henstock	NOUN
ejpam-5611	431	4	integration	integration	NOUN
ejpam-5611	431	5	on	on	ADP
ejpam-5611	431	6	manifolds	manifold	NOUN
ejpam-5611	431	7	.	.	PUNCT
ejpam-5611	432	1	taiwanese	taiwanese	ADJ
ejpam-5611	432	2	journal	journal	NOUN
ejpam-5611	432	3	of	of	ADP
ejpam-5611	432	4	mathematics	mathematic	NOUN
ejpam-5611	432	5	,	,	PUNCT
ejpam-5611	432	6	15(2):559–571	15(2):559–571	PROPN
ejpam-5611	432	7	,	,	PUNCT
ejpam-5611	432	8	2011	2011	NUM
ejpam-5611	432	9	.	.	PUNCT
ejpam-5611	433	1	[	[	X
ejpam-5611	433	2	3	3	X
ejpam-5611	433	3	]	]	X
ejpam-5611	433	4	g.	g.	PROPN
ejpam-5611	433	5	c.	c.	PROPN
ejpam-5611	433	6	flores	flores	PROPN
ejpam-5611	433	7	.	.	PUNCT
ejpam-5611	434	1	on	on	ADP
ejpam-5611	434	2	the	the	DET
ejpam-5611	434	3	pul	pul	NOUN
ejpam-5611	434	4	-	-	PUNCT
ejpam-5611	434	5	stieltjes	stieltjes	NOUN
ejpam-5611	434	6	integral	integral	ADJ
ejpam-5611	434	7	on	on	ADP
ejpam-5611	434	8	manifolds	manifold	NOUN
ejpam-5611	434	9	.	.	PUNCT
ejpam-5611	435	1	iranian	iranian	ADJ
ejpam-5611	435	2	journal	journal	PROPN
ejpam-5611	435	3	of	of	ADP
ejpam-5611	435	4	mathematical	mathematical	ADJ
ejpam-5611	435	5	sciences	sciences	PROPN
ejpam-5611	435	6	and	and	CCONJ
ejpam-5611	435	7	informatics	informatic	NOUN
ejpam-5611	435	8	.	.	PUNCT
ejpam-5611	436	1	to	to	PART
ejpam-5611	436	2	appear	appear	VERB
ejpam-5611	436	3	.	.	PUNCT
ejpam-5611	437	1	[	[	X
ejpam-5611	437	2	4	4	X
ejpam-5611	437	3	]	]	X
ejpam-5611	437	4	g.	g.	PROPN
ejpam-5611	437	5	c.	c.	PROPN
ejpam-5611	437	6	flores	flores	PROPN
ejpam-5611	437	7	and	and	CCONJ
ejpam-5611	437	8	j.	j.	PROPN
ejpam-5611	437	9	v.	v.	PROPN
ejpam-5611	437	10	benitez	benitez	PROPN
ejpam-5611	437	11	.	.	PUNCT
ejpam-5611	438	1	simple	simple	ADJ
ejpam-5611	438	2	properties	property	NOUN
ejpam-5611	438	3	of	of	ADP
ejpam-5611	438	4	pul	pul	NOUN
ejpam-5611	438	5	-	-	PUNCT
ejpam-5611	438	6	stieltjes	stieltjes	NOUN
ejpam-5611	438	7	integral	integral	ADJ
ejpam-5611	438	8	in	in	ADP
ejpam-5611	438	9	banach	banach	NOUN
ejpam-5611	438	10	space	space	NOUN
ejpam-5611	438	11	.	.	PUNCT
ejpam-5611	439	1	journal	journal	NOUN
ejpam-5611	439	2	of	of	ADP
ejpam-5611	439	3	ultra	ultra	ADJ
ejpam-5611	439	4	scientist	scientist	NOUN
ejpam-5611	439	5	of	of	ADP
ejpam-5611	439	6	physical	physical	ADJ
ejpam-5611	439	7	sciences	science	NOUN
ejpam-5611	439	8	,	,	PUNCT
ejpam-5611	439	9	29(4):126–134	29(4):126–134	PROPN
ejpam-5611	439	10	,	,	PUNCT
ejpam-5611	439	11	2017	2017	NUM
ejpam-5611	439	12	.	.	PUNCT
ejpam-5611	440	1	g.	g.	PROPN
ejpam-5611	440	2	flores	flores	PROPN
ejpam-5611	440	3	,	,	PUNCT
ejpam-5611	440	4	a.	a.	PROPN
ejpam-5611	440	5	flores	flores	PROPN
ejpam-5611	440	6	/	/	SYM
ejpam-5611	440	7	eur	eur	PROPN
ejpam-5611	440	8	.	.	PUNCT
ejpam-5611	441	1	j.	j.	PROPN
ejpam-5611	441	2	pure	pure	PROPN
ejpam-5611	441	3	appl	appl	PROPN
ejpam-5611	441	4	.	.	PROPN
ejpam-5611	441	5	math	math	PROPN
ejpam-5611	441	6	,	,	PUNCT
ejpam-5611	441	7	18	18	NUM
ejpam-5611	441	8	(	(	PUNCT
ejpam-5611	441	9	2	2	NUM
ejpam-5611	441	10	)	)	PUNCT
ejpam-5611	441	11	(	(	PUNCT
ejpam-5611	441	12	2025	2025	NUM
ejpam-5611	441	13	)	)	PUNCT
ejpam-5611	441	14	,	,	PUNCT
ejpam-5611	441	15	5611	5611	NUM
ejpam-5611	441	16	16	16	NUM
ejpam-5611	441	17	of	of	ADP
ejpam-5611	441	18	16	16	NUM
ejpam-5611	442	1	[	[	X
ejpam-5611	442	2	5	5	NUM
ejpam-5611	442	3	]	]	PUNCT
ejpam-5611	442	4	g.	g.	PROPN
ejpam-5611	442	5	c.	c.	PROPN
ejpam-5611	442	6	flores	flores	PROPN
ejpam-5611	442	7	and	and	CCONJ
ejpam-5611	442	8	j.	j.	PROPN
ejpam-5611	442	9	v.	v.	PROPN
ejpam-5611	442	10	benitez	benitez	PROPN
ejpam-5611	442	11	.	.	PUNCT
ejpam-5611	443	1	some	some	DET
ejpam-5611	443	2	convergence	convergence	NOUN
ejpam-5611	443	3	theorems	theorem	NOUN
ejpam-5611	443	4	of	of	ADP
ejpam-5611	443	5	the	the	DET
ejpam-5611	443	6	pul	pul	NOUN
ejpam-5611	443	7	-	-	PUNCT
ejpam-5611	443	8	stieltjes	stieltjes	NOUN
ejpam-5611	443	9	integral	integral	ADJ
ejpam-5611	443	10	.	.	PUNCT
ejpam-5611	444	1	iranian	iranian	ADJ
ejpam-5611	444	2	journal	journal	PROPN
ejpam-5611	444	3	of	of	ADP
ejpam-5611	444	4	mathematical	mathematical	ADJ
ejpam-5611	444	5	sciences	sciences	PROPN
ejpam-5611	444	6	and	and	CCONJ
ejpam-5611	444	7	informatics	informatic	NOUN
ejpam-5611	444	8	,	,	PUNCT
ejpam-5611	444	9	2(4):126–134	2(4):126–134	NUM
ejpam-5611	444	10	,	,	PUNCT
ejpam-5611	444	11	2021	2021	NUM
ejpam-5611	444	12	.	.	PUNCT
ejpam-5611	445	1	[	[	X
ejpam-5611	445	2	6	6	NUM
ejpam-5611	445	3	]	]	PUNCT
ejpam-5611	445	4	l.	l.	PROPN
ejpam-5611	445	5	t.	t.	PROPN
ejpam-5611	445	6	yeong	yeong	PROPN
ejpam-5611	445	7	.	.	PUNCT
ejpam-5611	445	8	series	series	PROPN
ejpam-5611	445	9	in	in	ADP
ejpam-5611	445	10	real	real	ADJ
ejpam-5611	445	11	analysis	analysis	NOUN
ejpam-5611	445	12	volume	volume	NOUN
ejpam-5611	445	13	12	12	NUM
ejpam-5611	445	14	:	:	PUNCT
ejpam-5611	445	15	henstock	henstock	NOUN
ejpam-5611	445	16	-	-	PUNCT
ejpam-5611	445	17	kurzweil	kurzweil	NOUN
ejpam-5611	445	18	integration	integration	NOUN
ejpam-5611	445	19	on	on	ADP
ejpam-5611	445	20	euclidean	euclidean	ADJ
ejpam-5611	445	21	spaces	space	NOUN
ejpam-5611	445	22	.	.	PUNCT
ejpam-5611	446	1	world	world	NOUN
ejpam-5611	446	2	scientific	scientific	PROPN
ejpam-5611	446	3	,	,	PUNCT
ejpam-5611	446	4	2011	2011	NUM
ejpam-5611	446	5	.	.	PUNCT
ejpam-5611	447	1	[	[	X
ejpam-5611	447	2	7	7	X
ejpam-5611	447	3	]	]	PUNCT
ejpam-5611	447	4	l.	l.	PROPN
ejpam-5611	447	5	w.	w.	PROPN
ejpam-5611	447	6	tu	tu	PROPN
ejpam-5611	447	7	.	.	PUNCT
ejpam-5611	448	1	an	an	DET
ejpam-5611	448	2	introduction	introduction	NOUN
ejpam-5611	448	3	to	to	ADP
ejpam-5611	448	4	manifolds	manifold	NOUN
ejpam-5611	448	5	.	.	PUNCT
ejpam-5611	449	1	springer	springer	NOUN
ejpam-5611	449	2	science	science	NOUN
ejpam-5611	449	3	+	+	CCONJ
ejpam-5611	449	4	business	business	NOUN
ejpam-5611	449	5	media	medium	NOUN
ejpam-5611	449	6	,	,	PUNCT
ejpam-5611	449	7	llc	llc	PROPN
ejpam-5611	449	8	.	.	PROPN
ejpam-5611	449	9	,	,	PUNCT
ejpam-5611	449	10	2008	2008	NUM
ejpam-5611	449	11	.	.	PUNCT